url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ (if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_) ∈
(fun a => if evalPrime V a then a else a.not_) '' Δ_U | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U,
(if evalPrime V x then x else x.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ (if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_) ∈
(fun a => if evalPrime V a then a else ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply Exists.intro F | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U,
(if evalPrime V x then x else x.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_ | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U,
(if evalPrime V x then x else x.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | tauto | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | let F := eq_ x y | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑(eq_ x y).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑(eq_ x y).primeSet ⊆ Δ_U
F : Formula := eq_ x y
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑(eq_ x y).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.primeSet] at h1 | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑(eq_ x y).primeSet ⊆ Δ_U
F : Formula := eq_ x y
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑{eq_ x y} ⊆ Δ_U
F : Formula := eq_ x y
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑(eq_ x y).primeSet ⊆ Δ_U
F : Formula := eq_ x y
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at h1 | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑{eq_ x y} ⊆ Δ_U
F : Formula := eq_ x y
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑{eq_ x y} ⊆ Δ_U
F : Formula := eq_ x y
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y)) | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (eq_ x y) then eq_ x y else (eq_ x y).not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.evalPrime] | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (eq_ x y) then eq_ x y else (eq_ x y).not_) | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (eq_ x y) then eq_ x y else (eq_ x y).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.assume_ | Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) | case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp | case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U | case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply Exists.intro F | case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_ | case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | tauto | case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
F : Formula := eq_ x y
h1 : eq_ x y ∈ Δ_U
⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.axiom_ | Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V true_) | case a
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsAxiom (evalPrimeFfToNot V true_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V true_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsAxiom.prop_true_ | case a
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsAxiom (evalPrimeFfToNot V true_) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsAxiom (evalPrimeFfToNot V true_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.primeSet] at h1 | Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑false_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_) | Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑∅ ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑false_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at h1 | Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑∅ ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_) | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑∅ ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_) | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V false_ then false_ else false_.not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.evalPrime] | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V false_ then false_ else false_.not_) | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then false_ else false_.not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V false_ then false_ else false_.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then false_ else false_.not_) | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) false_.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then false_ else false_.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | sorry | Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) false_.not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
h1 : True
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) false_.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.primeSet] at h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑phi.not_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_) | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑phi.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑phi.not_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑phi.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_) | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑phi.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_) | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V phi.not_... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct (evalPrimeFfToNot V '' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrime] | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V phi.not_... | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if ¬evalPrime V phi the... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if ¬evalPrime V phi the... | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | split_ifs | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi... | case pos
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h✝ : evalPrime V phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | case _ c1 =>
simp only [c1] at phi_ih
simp at phi_ih
apply IsDeduct.mp_ phi
apply proof_imp_deduct
apply T_14_6
exact phi_ih h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : evalPrime V phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : evalPrime V phi
⊢ IsDeduct ((... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | case _ c1 =>
simp only [c1] at phi_ih
simp at phi_ih
exact phi_ih h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : ¬evalPrime V phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.no... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : ¬evalPrime V phi
⊢ IsDeduct (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [c1] at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : evalPrime V phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not... | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if True then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : evalPrime V phi
⊢ IsDeduct ((... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if True then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_ | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if True then phi else phi.not_)
⊢ IsDeduct ((fun a => if... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.mp_ phi | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_ | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ phi.not_.not_)
case a
Δ_U : Set For... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply proof_imp_deduct | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ phi.not_.not_)
case a
Δ_U : Set For... | case a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsProof (phi.imp_ phi.not_.not_)
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.pri... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply T_14_6 | case a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsProof (phi.imp_ phi.not_.not_)
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.pri... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsProof (phi.imp_ phi.not_.not_)
case a
Δ_U : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | exact phi_ih h1 | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [c1] at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : ¬evalPrime V phi
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.no... | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
c1 : ¬evalPrime V phi
⊢ IsDeduct (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then phi else phi.not_)
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then phi else phi.not_)
⊢ IsDeduct ((fun a => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | exact phi_ih h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.primeSet] at h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑(phi.imp_ psi).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑(phi.primeSet ∪ psi.primeSet) ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑(phi.imp_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑(phi.primeSet ∪ psi.primeSet) ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑(phi.prim... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑phi.prime... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] at psi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi)
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if e... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | cases h1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime... | case intro
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | split_ifs | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | case pos
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if e... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | case _ c1 =>
simp only [evalPrime] at c1
simp only [imp_iff_not_or] at c1
cases c1
case _ c1 =>
simp only [if_neg c1] at phi_ih
apply IsDeduct.mp_ (not_ phi)
apply proof_imp_deduct
apply T_13_6
apply phi_ih h1_left
case _ c1 =>
simp only [if_pos c1] at psi_ih
apply IsDeduct.mp_ psi... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrime] at c1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [imp_iff_not_or] at c1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | cases c1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | case inl
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if e... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | case _ c1 =>
simp only [if_neg c1] at phi_ih
apply IsDeduct.mp_ (not_ phi)
apply proof_imp_deduct
apply T_13_6
apply phi_ih h1_left | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | case _ c1 =>
simp only [if_pos c1] at psi_ih
apply IsDeduct.mp_ psi
apply IsDeduct.axiom_
apply IsAxiom.prop_1_
apply psi_ih
exact h1_right | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [if_neg c1] at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → Is... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.mp_ (not_ phi) | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ_U → Is... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply proof_imp_deduct | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ... | case a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.pr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply T_13_6 | case a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply phi_ih h1_left | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : ¬evalPrime V phi
phi_ih : ↑phi.primeSet ⊆ Δ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.pr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [if_pos c1] at psi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsD... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.mp_ psi | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsD... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.axiom_ | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_... | case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.pr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsAxiom.prop_1_ | case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ ... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply psi_ih | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.pr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | exact h1_right | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1 : evalPrime V psi
psi_ih : ↑psi.primeSet ⊆ Δ_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.pr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrime] at c1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at c1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | cases c1 | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | case intro
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [if_pos c1_left] at phi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime ... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
phi_ih :
↑phi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_)
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [if_neg c1_right] at psi_ih | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
p... | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
psi_ih :
↑psi.primeSet ⊆ Δ_U →
IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_)
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.mp_ psi.not_ | Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a... | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.mp_ phi | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ... | case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduc... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply proof_imp_deduct | case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduc... | case a.a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDe... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a el... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply T_14_8 | case a.a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDe... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h1
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | exact phi_ih h1_left | case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduc... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a el... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | exact psi_ih h1_right | case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
phi psi : Formula
h1_left : ↑phi.primeSet ⊆ Δ_U
h1_right : ↑psi.primeSet ⊆ Δ_U
c1_left : evalPrime V phi
c1_right : ¬evalPrime V psi
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | let F := forall_ x phi | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (for... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.primeSet] at h1 | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑{forall_ x phi} ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at h1 | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑{forall_ x phi} ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑{forall_ x phi} ⊆ Δ_U
F : Formula := forall_ x phi
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (eva... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi)) | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (forall_ x phi) then... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.evalPrime] | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (forall_ x phi) then... | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (forall_ x phi) = true then fo... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.assume_ | Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (forall_ x phi) = true then fo... | case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ (if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_) ∈
(fun a => if eval... | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp | case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ (if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_) ∈
(fun a => if eval... | case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ ∃ x_1 ∈ Δ_U,
(if evalPrime V x_1 then x_1 else x_1.not_) =
if V (forall_ x phi) = true t... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ (if V (forall_ x phi) = true then for... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply Exists.intro F | case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ ∃ x_1 ∈ Δ_U,
(if evalPrime V x_1 then x_1 else x_1.not_) =
if V (forall_ x phi) = true t... | case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) = if V (forall_ x phi) = true then forall_ x p... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ ∃ x_1 ∈ Δ_U,
(if evalPrime V x_1 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | tauto | case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) = if V (forall_ x phi) = true then forall_ x p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
F : Formula := forall_ x phi
h1 : forall_ x phi ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | let F := def_ X xs | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑(def_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑(def_ X xs).primeSet ⊆ Δ_U
F : Formula := def_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑(def_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.primeSet] at h1 | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑(def_ X xs).primeSet ⊆ Δ_U
F : Formula := def_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑{def_ X xs} ⊆ Δ_U
F : Formula := def_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑(def_ X xs).primeSet ⊆ Δ_U
F : Formula := def_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp at h1 | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑{def_ X xs} ⊆ Δ_U
F : Formula := def_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑{def_ X xs} ⊆ Δ_U
F : Formula := def_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [evalPrimeFfToNot] | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs)) | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (def_ X xs) then def_ X xs else (def_ X xs).not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp only [Formula.evalPrime] | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (def_ X xs) then def_ X xs else (def_ X xs).not_) | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (def_ X xs) then def_ X xs else (def_ X xs).not_)
TACTIC... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply IsDeduct.assume_ | Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | simp | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | apply Exists.intro F | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_ | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | tauto | case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
F : Formula := def_ X xs
h1 : def_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.L_15_7 | [773, 1] | [916, 10] | sorry | Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : VarName
a✝ : Formula
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(exists_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (exists_ a✝¹ a✝)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : VarName
a✝ : Formula
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(exists_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (exis... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | apply IsDeduct.mp_ (U.not_.imp_ P) | P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ P | case a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ ((U.not_.imp_ P).imp_ P)
case a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ (U.not_.imp_ P) | Please generate a tactic in lean4 to solve the state.
STATE:
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | apply IsDeduct.mp_ (U.imp_ P) | case a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ ((U.not_.imp_ P).imp_ P) | case a.a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P))
case a.a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ (U.imp_ P) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ ((U.not_.imp_ P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | apply proof_imp_deduct | case a.a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P)) | case a.a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsProof ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | apply T_14_9 | case a.a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsProof ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsProof ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | apply deduction_theorem | case a.a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ (U.imp_ P) | case a.a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct (Δ ∪ {U}) P | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ (U.imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | exact h1 | case a.a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct (Δ ∪ {U}) P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct (Δ ∪ {U}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | apply deduction_theorem | case a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ (U.not_.imp_ P) | case a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct (Δ ∪ {U.not_}) P | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct Δ (U.not_.imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9_Deduct | [919, 1] | [933, 13] | exact h2 | case a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct (Δ ∪ {U.not_}) P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1
P U : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {U}) P
h2 : IsDeduct (Δ ∪ {U.not_}) P
⊢ IsDeduct (Δ ∪ {U.not_}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.evalPrimeFfToNot_of_function_updateIte_true | [936, 1] | [950, 38] | induction F | F F' : Formula
V : VarBoolAssignment
h1 : F.IsPrime
⊢ evalPrimeFfToNot (Function.updateITE V F' true) F = Function.updateITE (evalPrimeFfToNot V) F' F F | case pred_const_
F' : Formula
V : VarBoolAssignment
a✝¹ : PredName
a✝ : List VarName
h1 : (pred_const_ a✝¹ a✝).IsPrime
⊢ evalPrimeFfToNot (Function.updateITE V F' true) (pred_const_ a✝¹ a✝) =
Function.updateITE (evalPrimeFfToNot V) F' (pred_const_ a✝¹ a✝) (pred_const_ a✝¹ a✝)
case pred_var_
F' : Formula
V : VarBoo... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
V : VarBoolAssignment
h1 : F.IsPrime
⊢ evalPrimeFfToNot (Function.updateITE V F' true) F = Function.updateITE (evalPrimeFfToNot V) F' F F
TACTIC:
|
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