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/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_last_apply | [148, 1] | [151, 8] | simp only [snoc] | V : Type ?u.7787
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ snoc l x (last n) = x | V : Type ?u.7787
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ (if h : (last n).val < n then l { val := (last n).val, isLt := h } else x) = x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.7787
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ snoc l x (last n) = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_last_apply | [148, 1] | [151, 8] | aesop | V : Type ?u.7787
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ (if h : (last n).val < n then l { val := (last n).val, isLt := h } else x) = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.7787
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ (if h : (last n).val < n then l { val := (last n).val, isLt := h } else x) = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_apply | [154, 1] | [157, 8] | simp only [snoc] | V : Type ?u.8297
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ snoc l x { val := n, isLt := (_ : n < Nat.succ n) } = x | V : Type ?u.8297
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ (if h : n < n then l { val := n, isLt := (_ : { val := n, isLt := (_ : n < Nat.succ n) }.val < n) } else x) = x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.8297
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ snoc l x { val := n, isLt := (_ : n < Nat.succ n) } = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_apply | [154, 1] | [157, 8] | aesop | V : Type ?u.8297
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ (if h : n < n then l { val := n, isLt := (_ : { val := n, isLt := (_ : n < Nat.succ n) }.val < n) } else x) = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.8297
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x : α
⊢ (if h : n < n then l { val := n, isLt := (_ : { val := n, isLt := (_ : n < Nat.succ n) }.val < n) } else x) = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_two_apply | [160, 1] | [163, 8] | simp only [snoc] | V : Type ?u.8870
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y : α
⊢ snoc (snoc l x) y { val := n, isLt := (_ : n < n + (1 + 1)) } = x | V : Type ?u.8870
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y : α
⊢ (if h : n < n + 1 then
if h_1 : n < n then
l
{ val := n,
isLt := (_ : { val := n, isLt := (_ : { val := n, isLt := (_ : n < n + (1 + 1)) }.val < n + 1) }.val < n) }
else x
else y) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.8870
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y : α
⊢ snoc (snoc l x) y { val := n, isLt := (_ : n < n + (1 + 1)) } = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_two_apply | [160, 1] | [163, 8] | aesop | V : Type ?u.8870
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y : α
⊢ (if h : n < n + 1 then
if h_1 : n < n then
l
{ val := n,
isLt := (_ : { val := n, isLt := (_ : { val := n, isLt := (_ : n < n + (1 + 1)) }.val < n + 1) }.val < n) }
else x
else y) =
x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.8870
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y : α
⊢ (if h : n < n + 1 then
if h_1 : n < n then
l
{ val := n,
isLt := (_ : { val := n, isLt := (_ : { val := n, isLt := (_ : n < n + (1 + 1)) }.val < n + 1) }.val < n) }
else x
else y) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_three_apply | [166, 1] | [170, 8] | simp only [snoc] | V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
⊢ snoc (snoc (snoc l x) y) z { val := n, isLt := (_ : n < n + (2 + 1)) } = x | V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
⊢ (if h : n < n + 1 + 1 then
if h_1 : n < n + 1 then
if h_2 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt := (_ : { val := n, isLt := (_ : n < n + (2 + 1)) }.val < n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
⊢ snoc (snoc (snoc l x) y) z { val := n, isLt := (_ : n < n + (2 + 1)) } = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_three_apply | [166, 1] | [170, 8] | have : n < n + 1 + 1 := Nat.lt_add _ | V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
⊢ (if h : n < n + 1 + 1 then
if h_1 : n < n + 1 then
if h_2 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt := (_ : { val := n, isLt := (_ : n < n + (2 + 1)) }.val < n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z) =
x | V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 then
if h_1 : n < n + 1 then
if h_2 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt := (_ : { val := n, isLt := (_ : n < n + (2 + 1)) }.val < n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
⊢ (if h : n < n + 1 + 1 then
if h_1 : n < n + 1 then
if h_2 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt := (_ : { val := n, isLt := (_ : n < n + (2 + 1)) }.val < n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_three_apply | [166, 1] | [170, 8] | aesop | V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 then
if h_1 : n < n + 1 then
if h_2 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt := (_ : { val := n, isLt := (_ : n < n + (2 + 1)) }.val < n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z) =
x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.9943
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 then
if h_1 : n < n + 1 then
if h_2 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt := (_ : { val := n, isLt := (_ : n < n + (2 + 1)) }.val < n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_four_apply | [173, 1] | [179, 8] | simp only [snoc] | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
⊢ snoc (snoc (snoc (snoc l x) y) z) w { val := n, isLt := (_ : n < n + (3 + 1)) } = x | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
⊢ snoc (snoc (snoc (snoc l x) y) z) w { val := n, isLt := (_ : n < n + (3 + 1)) } = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_four_apply | [173, 1] | [179, 8] | have : n < n + 1 + 1 := Nat.lt_add _ | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_four_apply | [173, 1] | [179, 8] | have : n < n + 1 + 1 + 1 := Nat.lt_add _ | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
this✝ : n < n + 1 + 1
this : n < n + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_four_apply | [173, 1] | [179, 8] | aesop | V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
this✝ : n < n + 1 + 1
this : n < n + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.11812
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w : α
this✝ : n < n + 1 + 1
this : n < n + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 then
if h_2 : n < n + 1 then
if h_3 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (3 + 1)) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_five_apply | [182, 1] | [189, 8] | simp only [snoc] | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
⊢ snoc (snoc (snoc (snoc (snoc l x) y) z) w) u { val := n, isLt := (_ : n < n + (4 + 1)) } = x | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
⊢ snoc (snoc (snoc (snoc (snoc l x) y) z) w) u { val := n, isLt := (_ : n < n + (4 + 1)) } = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_five_apply | [182, 1] | [189, 8] | have : n < n + 1 + 1 := Nat.lt_add _ | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_five_apply | [182, 1] | [189, 8] | have : n < n + 1 + 1 + 1 := Nat.lt_add _ | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this✝ : n < n + 1 + 1
this : n < n + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this : n < n + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_five_apply | [182, 1] | [189, 8] | have : n < n + 1 + 1 + 1 + 1 := Nat.lt_add _ | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this✝ : n < n + 1 + 1
this : n < n + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this✝¹ : n < n + 1 + 1
this✝ : n < n + 1 + 1 + 1
this : n < n + 1 + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this✝ : n < n + 1 + 1
this : n < n + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | Fin.snoc_five_apply | [182, 1] | [189, 8] | aesop | V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this✝¹ : n < n + 1 + 1
this✝ : n < n + 1 + 1 + 1
this : n < n + 1 + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type ?u.14957
inst✝ : SetTheory V
n : Nat
α : Sort u_1
l : Fin n → α
x y z w u : α
this✝¹ : n < n + 1 + 1
this✝ : n < n + 1 + 1 + 1
this : n < n + 1 + 1 + 1 + 1
⊢ (if h : n < n + 1 + 1 + 1 + 1 then
if h_1 : n < n + 1 + 1 + 1 then
if h_2 : n < n + 1 + 1 then
if h_3 : n < n + 1 then
if h_4 : n < n then
l
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n,
isLt :=
(_ :
{ val := n, isLt := (_ : n < n + (4 + 1)) }.val <
n + 1 + 1 + 1 + 1) }.val <
n + 1 + 1 + 1) }.val <
n + 1 + 1) }.val <
n + 1) }.val <
n) }
else x
else y
else z
else w
else u) =
x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_snoc_termSucc | [238, 1] | [240, 11] | aesop | V : Type u_2
inst✝ : SetTheory V
α✝ : Type u_1
v : α✝ → V
n✝ : Nat
l : Fin n✝ → V
y : V
x : α✝ ⊕ Fin n✝
⊢ interpretTerm V v (Fin.snoc l y) (termSucc x) = interpretTerm V v l x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_2
inst✝ : SetTheory V
α✝ : Type u_1
v : α✝ → V
n✝ : Nat
l : Fin n✝ → V
y : V
x : α✝ ⊕ Fin n✝
⊢ interpretTerm V v (Fin.snoc l y) (termSucc x) = interpretTerm V v l x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_termSum_elim | [271, 1] | [274, 21] | cases p <;> rfl | V : Type u_3
inst✝ : SetTheory V
α : Type u_1
n : Nat
vα : α → V
β✝ : Type u_2
vβ : β✝ → V
l : Fin n → V
p : α ⊕ Fin n
⊢ interpretTerm V (Sum.elim vα vβ) l (termSum p) = interpretTerm V vα l p | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_3
inst✝ : SetTheory V
α : Type u_1
n : Nat
vα : α → V
β✝ : Type u_2
vβ : β✝ → V
l : Fin n → V
p : α ⊕ Fin n
⊢ interpretTerm V (Sum.elim vα vβ) l (termSum p) = interpretTerm V vα l p
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_sum_elim | [277, 1] | [280, 27] | induction p <;> aesop | V : Type u_1
inst✝ : SetTheory V
β α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ a✝
vα : α✝ → V
vβ : β → V
l : Fin a✝ → V
⊢ Interpret V (sum β p) (Sum.elim vα vβ) l ↔ Interpret V p vα l | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
β α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ a✝
vα : α✝ → V
vβ : β → V
l : Fin a✝ → V
⊢ Interpret V (sum β p) (Sum.elim vα vβ) l ↔ Interpret V p vα l
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_or | [304, 1] | [307, 6] | rw [or_iff] | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.or p q) v l ↔ Interpret V p v l ∨ Interpret V q v l | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.or p q) v l ↔ ¬Interpret V p v l → Interpret V q v l | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.or p q) v l ↔ Interpret V p v l ∨ Interpret V q v l
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_or | [304, 1] | [307, 6] | rfl | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.or p q) v l ↔ ¬Interpret V p v l → Interpret V q v l | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.or p q) v l ↔ ¬Interpret V p v l → Interpret V q v l
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_and | [313, 1] | [316, 6] | rw [and_iff] | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and p q) v l ↔ Interpret V p v l ∧ Interpret V q v l | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and p q) v l ↔ ¬(Interpret V p v l → ¬Interpret V q v l) | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and p q) v l ↔ Interpret V p v l ∧ Interpret V q v l
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_and | [313, 1] | [316, 6] | rfl | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and p q) v l ↔ ¬(Interpret V p v l → ¬Interpret V q v l) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and p q) v l ↔ ¬(Interpret V p v l → ¬Interpret V q v l)
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_iff | [322, 1] | [325, 8] | unfold BoundedFormula.iff | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.iff p q) v l ↔ (Interpret V p v l ↔ Interpret V q v l) | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and (BoundedFormula.imp p q) (BoundedFormula.imp q p)) v l ↔
(Interpret V p v l ↔ Interpret V q v l) | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.iff p q) v l ↔ (Interpret V p v l ↔ Interpret V q v l)
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_iff | [322, 1] | [325, 8] | aesop | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and (BoundedFormula.imp p q) (BoundedFormula.imp q p)) v l ↔
(Interpret V p v l ↔ Interpret V q v l) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p q : BoundedFormula α✝ a✝
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.and (BoundedFormula.imp p q) (BoundedFormula.imp q p)) v l ↔
(Interpret V p v l ↔ Interpret V q v l)
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_subset | [333, 1] | [337, 8] | unfold BoundedFormula.subset | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
n✝ : Nat
x y : α✝ ⊕ Fin n✝
v : α✝ → V
l : Fin n✝ → V
⊢ Interpret V (BoundedFormula.subset x y) v l ↔ interpretTerm V v l x ⊆ interpretTerm V v l y | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
n✝ : Nat
x y : α✝ ⊕ Fin n✝
v : α✝ → V
l : Fin n✝ → V
⊢ Interpret V
(BoundedFormula.all
(BoundedFormula.imp (BoundedFormula.mem (Sum.inr (Fin.last n✝)) (termSucc x))
(BoundedFormula.mem (Sum.inr (Fin.last n✝)) (termSucc y))))
v l ↔
interpretTerm V v l x ⊆ interpretTerm V v l y | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
n✝ : Nat
x y : α✝ ⊕ Fin n✝
v : α✝ → V
l : Fin n✝ → V
⊢ Interpret V (BoundedFormula.subset x y) v l ↔ interpretTerm V v l x ⊆ interpretTerm V v l y
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_subset | [333, 1] | [337, 8] | aesop | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
n✝ : Nat
x y : α✝ ⊕ Fin n✝
v : α✝ → V
l : Fin n✝ → V
⊢ Interpret V
(BoundedFormula.all
(BoundedFormula.imp (BoundedFormula.mem (Sum.inr (Fin.last n✝)) (termSucc x))
(BoundedFormula.mem (Sum.inr (Fin.last n✝)) (termSucc y))))
v l ↔
interpretTerm V v l x ⊆ interpretTerm V v l y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
n✝ : Nat
x y : α✝ ⊕ Fin n✝
v : α✝ → V
l : Fin n✝ → V
⊢ Interpret V
(BoundedFormula.all
(BoundedFormula.imp (BoundedFormula.mem (Sum.inr (Fin.last n✝)) (termSucc x))
(BoundedFormula.mem (Sum.inr (Fin.last n✝)) (termSucc y))))
v l ↔
interpretTerm V v l x ⊆ interpretTerm V v l y
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_exists | [343, 1] | [347, 8] | unfold BoundedFormula.exists | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ (a✝ + 1)
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.exists p) v l ↔ ∃ x, Interpret V p v (Fin.snoc l x) | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ (a✝ + 1)
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.not (BoundedFormula.all (BoundedFormula.not p))) v l ↔ ∃ x, Interpret V p v (Fin.snoc l x) | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ (a✝ + 1)
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.exists p) v l ↔ ∃ x, Interpret V p v (Fin.snoc l x)
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Formula.lean | SetTheory.interpret_exists | [343, 1] | [347, 8] | aesop | V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ (a✝ + 1)
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.not (BoundedFormula.all (BoundedFormula.not p))) v l ↔ ∃ x, Interpret V p v (Fin.snoc l x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝ : SetTheory V
α✝ : Type
a✝ : Nat
p : BoundedFormula α✝ (a✝ + 1)
v : α✝ → V
l : Fin a✝ → V
⊢ Interpret V (BoundedFormula.not (BoundedFormula.all (BoundedFormula.not p))) v l ↔ ∃ x, Interpret V p v (Fin.snoc l x)
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Axioms.lean | SetTheory.ext_iff | [67, 1] | [69, 37] | aesop | V : Type u_1
inst✝² inst✝¹ : SetTheory V
inst✝ : Extensionality V
x y : V
⊢ x = y → ∀ (z : V), z ∈ x ↔ z ∈ y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝² inst✝¹ : SetTheory V
inst✝ : Extensionality V
x y : V
⊢ x = y → ∀ (z : V), z ∈ x ↔ z ∈ y
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Axioms.lean | SetTheory.mem_singleton_iff | [82, 1] | [85, 7] | show y ∈ pair x x ↔ y = x | V : Type u_1
inst✝² inst✝¹ : SetTheory V
y x : V
inst✝ : Pairing V
⊢ y ∈ {x} ↔ y = x | V : Type u_1
inst✝² inst✝¹ : SetTheory V
y x : V
inst✝ : Pairing V
⊢ y ∈ pair x x ↔ y = x | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝² inst✝¹ : SetTheory V
y x : V
inst✝ : Pairing V
⊢ y ∈ {x} ↔ y = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Axioms.lean | SetTheory.mem_singleton_iff | [82, 1] | [85, 7] | simp | V : Type u_1
inst✝² inst✝¹ : SetTheory V
y x : V
inst✝ : Pairing V
⊢ y ∈ pair x x ↔ y = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝² inst✝¹ : SetTheory V
y x : V
inst✝ : Pairing V
⊢ y ∈ pair x x ↔ y = x
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Axioms.lean | SetTheory.mem_union_iff | [100, 1] | [103, 8] | show z ∈ ⋃ pair x y ↔ z ∈ x ∨ z ∈ y | V : Type u_1
inst✝³ inst✝² : SetTheory V
inst✝¹ : Union V
inst✝ : Pairing V
x y z : V
⊢ z ∈ x ∪ y ↔ z ∈ x ∨ z ∈ y | V : Type u_1
inst✝³ inst✝² : SetTheory V
inst✝¹ : Union V
inst✝ : Pairing V
x y z : V
⊢ z ∈ ⋃ pair x y ↔ z ∈ x ∨ z ∈ y | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝³ inst✝² : SetTheory V
inst✝¹ : Union V
inst✝ : Pairing V
x y z : V
⊢ z ∈ x ∪ y ↔ z ∈ x ∨ z ∈ y
TACTIC:
|
https://github.com/zeramorphic/set-theory.git | 37e9d6e920ff687317f50fa33984b273f1637716 | SetTheory/Axioms.lean | SetTheory.mem_union_iff | [100, 1] | [103, 8] | aesop | V : Type u_1
inst✝³ inst✝² : SetTheory V
inst✝¹ : Union V
inst✝ : Pairing V
x y z : V
⊢ z ∈ ⋃ pair x y ↔ z ∈ x ∨ z ∈ y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
V : Type u_1
inst✝³ inst✝² : SetTheory V
inst✝¹ : Union V
inst✝ : Pairing V
x y z : V
⊢ z ∈ ⋃ pair x y ↔ z ∈ x ∨ z ∈ y
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.mop_injective' | [18, 1] | [22, 14] | constructor | ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q ↔ p = q | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q → p = q
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q ↔ p = q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.mop_injective' | [18, 1] | [22, 14] | . intro h; exact mop_injective h; | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q → p = q
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q | case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q → p = q
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.mop_injective' | [18, 1] | [22, 14] | . simp_all; | case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.mop_injective' | [18, 1] | [22, 14] | intro h | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q → p = q | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
h : mop i p = mop i q
⊢ p = q | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ mop i p = mop i q → p = q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.mop_injective' | [18, 1] | [22, 14] | exact mop_injective h | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
h : mop i p = mop i q
⊢ p = q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
h : mop i p = mop i q
⊢ p = q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.mop_injective' | [18, 1] | [22, 14] | simp_all | case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
⊢ p = q → mop i p = mop i q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_succ | [24, 1] | [24, 108] | apply iterate_succ_apply' | ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n + 1] p = mop i ((mop i)^[n] p) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n + 1] p = mop i ((mop i)^[n] p)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective | [26, 1] | [26, 128] | apply Function.Injective.iterate (by simp) | ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ Injective (mop i)^[n] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ Injective (mop i)^[n]
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective | [26, 1] | [26, 128] | simp | ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ Injective (mop i) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ Injective (mop i)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective' | [28, 1] | [32, 14] | constructor | ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q ↔ p = q | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q → p = q
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q ↔ p = q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective' | [28, 1] | [32, 14] | . intro h; exact multimop_injective h; | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q → p = q
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q | case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q → p = q
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective' | [28, 1] | [32, 14] | . simp_all; | case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective' | [28, 1] | [32, 14] | intro h | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q → p = q | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
h : (mop i)^[n] p = (mop i)^[n] q
⊢ p = q | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ (mop i)^[n] p = (mop i)^[n] q → p = q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective' | [28, 1] | [32, 14] | exact multimop_injective h | case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
h : (mop i)^[n] p = (mop i)^[n] q
⊢ p = q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
h : (mop i)^[n] p = (mop i)^[n] q
⊢ p = q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.UnaryModalOperator.multimop_injective' | [28, 1] | [32, 14] | simp_all | case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
ι : Type u_2
F : Type u_1
inst✝ : UnaryModalOperator ι F
i : ι
p q : F
n : ℕ
⊢ p = q → (mop i)^[n] p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.mop_iff_multimop_one | [59, 1] | [59, 72] | rfl | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
⊢ Set.mop i s = Set.multimop i 1 s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
⊢ Set.mop i s = Set.multimop i 1 s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.premop_iff_premultimop_one | [61, 1] | [61, 84] | rfl | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
⊢ Set.premop i s = Set.premultimop i 1 s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
⊢ Set.premop i s = Set.premultimop i 1 s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.multimop_subset | [64, 1] | [64, 101] | simp_all [Set.subset_def] | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ t
⊢ Set.multimop i n s ⊆ Set.multimop i n t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ t
⊢ Set.multimop i n s ⊆ Set.multimop i n t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.premultimop_subset | [66, 1] | [66, 110] | simp_all [Set.subset_def] | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ t
⊢ Set.premultimop i n s ⊆ Set.premultimop i n t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ t
⊢ Set.premultimop i n s ⊆ Set.premultimop i n t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_premulitimop_iff_multimop_subset | [68, 1] | [72, 14] | intro p hp | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
⊢ Set.multimop i n s ⊆ t | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
p : F
hp : p ∈ Set.multimop i n s
⊢ p ∈ t | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
⊢ Set.multimop i n s ⊆ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_premulitimop_iff_multimop_subset | [68, 1] | [72, 14] | obtain ⟨_, h₁, h₂⟩ := multimop_subset h hp | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
p : F
hp : p ∈ Set.multimop i n s
⊢ p ∈ t | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
p : F
hp : p ∈ Set.multimop i n s
w✝ : F
h₁ : w✝ ∈ Set.premultimop i n t
h₂ : (mop i)^[n] w✝ = p
⊢ p ∈ t | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
p : F
hp : p ∈ Set.multimop i n s
⊢ p ∈ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_premulitimop_iff_multimop_subset | [68, 1] | [72, 14] | subst h₂ | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
p : F
hp : p ∈ Set.multimop i n s
w✝ : F
h₁ : w✝ ∈ Set.premultimop i n t
h₂ : (mop i)^[n] w✝ = p
⊢ p ∈ t | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
w✝ : F
h₁ : w✝ ∈ Set.premultimop i n t
hp : (mop i)^[n] w✝ ∈ Set.multimop i n s
⊢ (mop i)^[n] w✝ ∈ t | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
p : F
hp : p ∈ Set.multimop i n s
w✝ : F
h₁ : w✝ ∈ Set.premultimop i n t
h₂ : (mop i)^[n] w✝ = p
⊢ p ∈ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_premulitimop_iff_multimop_subset | [68, 1] | [72, 14] | assumption | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
w✝ : F
h₁ : w✝ ∈ Set.premultimop i n t
hp : (mop i)^[n] w✝ ∈ Set.multimop i n s
⊢ (mop i)^[n] w✝ ∈ t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.premultimop i n t
w✝ : F
h₁ : w✝ ∈ Set.premultimop i n t
hp : (mop i)^[n] w✝ ∈ Set.multimop i n s
⊢ (mop i)^[n] w✝ ∈ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_multimop_iff_premulitimop_subset | [74, 1] | [77, 12] | intro p hp | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.premultimop i n s ⊆ t | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.premultimop i n s
⊢ p ∈ t | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.premultimop i n s ⊆ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_multimop_iff_premulitimop_subset | [74, 1] | [77, 12] | obtain ⟨_, h₁, h₂⟩ := premultimop_subset h hp | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.premultimop i n s
⊢ p ∈ t | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.premultimop i n s
w✝ : F
h₁ : w✝ ∈ t
h₂ : (mop i)^[n] w✝ = (mop i)^[n] p
⊢ p ∈ t | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.premultimop i n s
⊢ p ∈ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.subset_multimop_iff_premulitimop_subset | [74, 1] | [77, 12] | simp_all | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.premultimop i n s
w✝ : F
h₁ : w✝ ∈ t
h₂ : (mop i)^[n] w✝ = (mop i)^[n] p
⊢ p ∈ t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.premultimop i n s
w✝ : F
h₁ : w✝ ∈ t
h₂ : (mop i)^[n] w✝ = (mop i)^[n] p
⊢ p ∈ t
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.forall_multimop_of_subset_multimop | [79, 1] | [83, 12] | intro p hp | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ ∀ p ∈ s, ∃ q ∈ t, p = (mop i)^[n] q | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
⊢ ∃ q ∈ t, p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ ∀ p ∈ s, ∃ q ∈ t, p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.forall_multimop_of_subset_multimop | [79, 1] | [83, 12] | obtain ⟨q, hq₁, hq₂⟩ := h hp | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
⊢ ∃ q ∈ t, p = (mop i)^[n] q | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
hq₁ : q ∈ t
hq₂ : (mop i)^[n] q = p
⊢ ∃ q ∈ t, p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
⊢ ∃ q ∈ t, p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.forall_multimop_of_subset_multimop | [79, 1] | [83, 12] | use q | case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
hq₁ : q ∈ t
hq₂ : (mop i)^[n] q = p
⊢ ∃ q ∈ t, p = (mop i)^[n] q | case h
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
hq₁ : q ∈ t
hq₂ : (mop i)^[n] q = p
⊢ q ∈ t ∧ p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
hq₁ : q ∈ t
hq₂ : (mop i)^[n] q = p
⊢ ∃ q ∈ t, p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.forall_multimop_of_subset_multimop | [79, 1] | [83, 12] | simp_all | case h
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
hq₁ : q ∈ t
hq₂ : (mop i)^[n] q = p
⊢ q ∈ t ∧ p = (mop i)^[n] q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
hq₁ : q ∈ t
hq₂ : (mop i)^[n] q = p
⊢ q ∈ t ∧ p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | apply Set.eq_of_subset_of_subset | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) = s | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) ⊆ s
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s) | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) = s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | . intro p hp;
obtain ⟨q, hq₁, hq₂⟩ := hp;
simp_all [Set.premultimop]; | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) ⊆ s
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s) | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) ⊆ s
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | . intro p hp;
obtain ⟨q, _, hq₂⟩ := forall_multimop_of_subset_multimop h p hp;
simp_all [Set.premultimop]; | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | intro p hp | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) ⊆ s | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.multimop i n (Set.premultimop i n s)
⊢ p ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ Set.multimop i n (Set.premultimop i n s) ⊆ s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | obtain ⟨q, hq₁, hq₂⟩ := hp | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.multimop i n (Set.premultimop i n s)
⊢ p ∈ s | case a.intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p q : F
hq₁ : q ∈ Set.premultimop i n s
hq₂ : (mop i)^[n] q = p
⊢ p ∈ s | Please generate a tactic in lean4 to solve the state.
STATE:
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ Set.multimop i n (Set.premultimop i n s)
⊢ p ∈ s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | simp_all [Set.premultimop] | case a.intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p q : F
hq₁ : q ∈ Set.premultimop i n s
hq₂ : (mop i)^[n] q = p
⊢ p ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p q : F
hq₁ : q ∈ Set.premultimop i n s
hq₂ : (mop i)^[n] q = p
⊢ p ∈ s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | intro p hp | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s) | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
⊢ p ∈ Set.multimop i n (Set.premultimop i n s) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Set F
h : s ⊆ Set.multimop i n t
⊢ s ⊆ Set.multimop i n (Set.premultimop i n s)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | obtain ⟨q, _, hq₂⟩ := forall_multimop_of_subset_multimop h p hp | case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
⊢ p ∈ Set.multimop i n (Set.premultimop i n s) | case a.intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
left✝ : q ∈ t
hq₂ : p = (mop i)^[n] q
⊢ p ∈ Set.multimop i n (Set.premultimop i n s) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
⊢ p ∈ Set.multimop i n (Set.premultimop i n s)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Set.eq_premultimop_multimop_of_subset_premultimop | [85, 1] | [92, 32] | simp_all [Set.premultimop] | case a.intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
left✝ : q ∈ t
hq₂ : p = (mop i)^[n] q
⊢ p ∈ Set.multimop i n (Set.premultimop i n s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.intro.intro
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
s t : Set F
h : s ⊆ Set.multimop i n t
p : F
hp : p ∈ s
q : F
left✝ : q ∈ t
hq₂ : p = (mop i)^[n] q
⊢ p ∈ Set.multimop i n (Set.premultimop i n s)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.iff_mop_multimop_one | [109, 1] | [109, 73] | rfl | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ Finset.mop i s = Finset.multimop i 1 s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ Finset.mop i s = Finset.multimop i 1 s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.iff_premop_premultimop_one | [111, 1] | [111, 85] | rfl | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ Finset.premop i s = Finset.premultimop i 1 s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ Finset.premop i s = Finset.premultimop i 1 s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.multimop_coe | [114, 1] | [114, 83] | simp_all | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ ↑(Finset.multimop i n s) = Set.multimop i n ↑s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ ↑(Finset.multimop i n s) = Set.multimop i n ↑s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.multimop_mem_coe | [116, 1] | [116, 107] | constructor <;> simp_all | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ p ∈ Finset.multimop i n s ↔ p ∈ Set.multimop i n ↑s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ p ∈ Finset.multimop i n s ↔ p ∈ Set.multimop i n ↑s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.premultimop_coe | [118, 1] | [118, 109] | apply Finset.coe_preimage | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ ↑(Finset.premultimop i n s) = Set.premultimop i n ↑s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s t : Finset F
⊢ ↑(Finset.premultimop i n s) = Set.premultimop i n ↑s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.premultimop_multimop_eq_of_subset_multimop | [120, 1] | [123, 32] | have := Set.eq_premultimop_multimop_of_subset_premultimop hs | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
⊢ Finset.multimop i n (Finset.premultimop i n s) = s | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
this : Set.multimop i n (Set.premultimop i n ↑s) = ↑s
⊢ Finset.multimop i n (Finset.premultimop i n s) = s | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
⊢ Finset.multimop i n (Finset.premultimop i n s) = s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.premultimop_multimop_eq_of_subset_multimop | [120, 1] | [123, 32] | rw [←premultimop_coe, ←multimop_coe] at this | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
this : Set.multimop i n (Set.premultimop i n ↑s) = ↑s
⊢ Finset.multimop i n (Finset.premultimop i n s) = s | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
this : ↑(Finset.multimop i n (Finset.premultimop i n s)) = ↑s
⊢ Finset.multimop i n (Finset.premultimop i n s) = s | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
this : Set.multimop i n (Set.premultimop i n ↑s) = ↑s
⊢ Finset.multimop i n (Finset.premultimop i n s) = s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | Finset.premultimop_multimop_eq_of_subset_multimop | [120, 1] | [123, 32] | exact Finset.coe_inj.mp this | ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
this : ↑(Finset.multimop i n (Finset.premultimop i n s)) = ↑s
⊢ Finset.multimop i n (Finset.premultimop i n s) = s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
i : ι
n : ℕ
p q : F
s✝ t✝ s : Finset F
t : Set F
hs : ↑s ⊆ Set.multimop i n t
this : ↑(Finset.multimop i n (Finset.premultimop i n s)) = ↑s
⊢ Finset.multimop i n (Finset.premultimop i n s) = s
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.mop_iff_multimop_one | [142, 1] | [142, 72] | rfl | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.mop i l = List.multimop i 1 l | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.mop i l = List.multimop i 1 l
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.iff_premop_premultimop_one | [144, 1] | [144, 84] | rfl | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.premop i l = List.premultimop i 1 l | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.premop i l = List.premultimop i 1 l
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.multimop_nil | [146, 1] | [146, 74] | simp | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.multimop i n [] = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.multimop i n [] = []
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.multimop_single | [148, 1] | [148, 93] | simp | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.multimop i n [p] = [(mop i)^[n] p] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.multimop i n [p] = [(mop i)^[n] p]
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.multimop_cons | [150, 1] | [153, 12] | simp [List.multimop] | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ List.multimop i n (p :: l) ~ (mop i)^[n] p :: List.multimop i n l | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ (insert ((mop i)^[n] p) (Finset.image (mop i)^[n] l.toFinset)).toList ~
(mop i)^[n] p :: (Finset.multimop i n l.toFinset).toList | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ List.multimop i n (p :: l) ~ (mop i)^[n] p :: List.multimop i n l
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.multimop_cons | [150, 1] | [153, 12] | apply Finset.toList_insert | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ (insert ((mop i)^[n] p) (Finset.image (mop i)^[n] l.toFinset)).toList ~
(mop i)^[n] p :: (Finset.multimop i n l.toFinset).toList | case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ (mop i)^[n] p ∉ Finset.image (mop i)^[n] l.toFinset | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ (insert ((mop i)^[n] p) (Finset.image (mop i)^[n] l.toFinset)).toList ~
(mop i)^[n] p :: (Finset.multimop i n l.toFinset).toList
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.multimop_cons | [150, 1] | [153, 12] | simp_all | case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ (mop i)^[n] p ∉ Finset.image (mop i)^[n] l.toFinset | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
hl : p ∉ l
⊢ (mop i)^[n] p ∉ Finset.image (mop i)^[n] l.toFinset
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.premultimop_nil | [155, 1] | [155, 80] | simp | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.premultimop i n [] = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
⊢ List.premultimop i n [] = []
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.forall_multimop_of_subset_multimop | [157, 1] | [160, 28] | intro p hp | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
⊢ ∀ p ∈ l, ∃ q ∈ s, p = (mop i)^[n] q | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
⊢ ∃ q ∈ s, p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
⊢ ∀ p ∈ l, ∃ q ∈ s, p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.forall_multimop_of_subset_multimop | [157, 1] | [160, 28] | obtain ⟨q, _, _⟩ := by simpa only [Set.mem_image] using h p hp; | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
⊢ ∃ q ∈ s, p = (mop i)^[n] q | case intro.intro
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
q : F
left✝ : q ∈ s
right✝ : (mop i)^[n] q = p
⊢ ∃ q ∈ s, p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
⊢ ∃ q ∈ s, p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.forall_multimop_of_subset_multimop | [157, 1] | [160, 28] | use q | case intro.intro
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
q : F
left✝ : q ∈ s
right✝ : (mop i)^[n] q = p
⊢ ∃ q ∈ s, p = (mop i)^[n] q | case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
q : F
left✝ : q ∈ s
right✝ : (mop i)^[n] q = p
⊢ q ∈ s ∧ p = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
q : F
left✝ : q ∈ s
right✝ : (mop i)^[n] q = p
⊢ ∃ q ∈ s, p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.forall_multimop_of_subset_multimop | [157, 1] | [160, 28] | subst_vars | case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
q : F
left✝ : q ∈ s
right✝ : (mop i)^[n] q = p
⊢ q ∈ s ∧ p = (mop i)^[n] q | case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
q : F
left✝ : q ∈ s
hp : (mop i)^[n] q ∈ l
⊢ q ∈ s ∧ (mop i)^[n] q = (mop i)^[n] q | Please generate a tactic in lean4 to solve the state.
STATE:
case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
q : F
left✝ : q ∈ s
right✝ : (mop i)^[n] q = p
⊢ q ∈ s ∧ p = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.forall_multimop_of_subset_multimop | [157, 1] | [160, 28] | simpa | case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
q : F
left✝ : q ∈ s
hp : (mop i)^[n] q ∈ l
⊢ q ∈ s ∧ (mop i)^[n] q = (mop i)^[n] q | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p q✝ : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
q : F
left✝ : q ∈ s
hp : (mop i)^[n] q ∈ l
⊢ q ∈ s ∧ (mop i)^[n] q = (mop i)^[n] q
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | List.forall_multimop_of_subset_multimop | [157, 1] | [160, 28] | simpa only [Set.mem_image] using h p hp | ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
⊢ ?m.51038 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
ι : Type u_2
F : Type u_1
inst✝³ : UnaryModalOperator ι F
inst✝² : DecidableEq F
i : ι
n : ℕ
p✝ q : F
inst✝¹ : UnaryModalOperator ι F
inst✝ : DecidableEq F
l : List F
s : Set F
h : ∀ p ∈ l, p ∈ Set.multimop i n s
p : F
hp : p ∈ l
⊢ ?m.51038
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Modal/LogicSymbol.lean | LO.StandardModalLogicalConnective.duality' | [193, 1] | [193, 61] | apply duality | F : Type u_1
inst✝ : StandardModalLogicalConnective F
p : F
⊢ ◇p = ~(□~p) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Type u_1
inst✝ : StandardModalLogicalConnective F
p : F
⊢ ◇p = ~(□~p)
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Completeness/Lemmata.lean | LO.FirstOrder.ModelsTheory.of_provably_subtheory | [9, 1] | [12, 54] | intro p hp | L : Language
M : Type w
inst✝¹ : Nonempty M
inst✝ : Structure L M
T U V : Theory L
x✝ : T ≼ U
h : M ⊧ₘ* U
⊢ ∀ ⦃f : Sentence L⦄, f ∈ T → inst✝.toStruc ⊧ f | L : Language
M : Type w
inst✝¹ : Nonempty M
inst✝ : Structure L M
T U V : Theory L
x✝ : T ≼ U
h : M ⊧ₘ* U
p : Sentence L
hp : p ∈ T
⊢ inst✝.toStruc ⊧ p | Please generate a tactic in lean4 to solve the state.
STATE:
L : Language
M : Type w
inst✝¹ : Nonempty M
inst✝ : Structure L M
T U V : Theory L
x✝ : T ≼ U
h : M ⊧ₘ* U
⊢ ∀ ⦃f : Sentence L⦄, f ∈ T → inst✝.toStruc ⊧ f
TACTIC:
|
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Completeness/Lemmata.lean | LO.FirstOrder.ModelsTheory.of_provably_subtheory | [9, 1] | [12, 54] | have : U ⊢ p := System.Subtheory.prf (System.byAxm hp) | L : Language
M : Type w
inst✝¹ : Nonempty M
inst✝ : Structure L M
T U V : Theory L
x✝ : T ≼ U
h : M ⊧ₘ* U
p : Sentence L
hp : p ∈ T
⊢ inst✝.toStruc ⊧ p | L : Language
M : Type w
inst✝¹ : Nonempty M
inst✝ : Structure L M
T U V : Theory L
x✝ : T ≼ U
h : M ⊧ₘ* U
p : Sentence L
hp : p ∈ T
this : U ⊢ p
⊢ inst✝.toStruc ⊧ p | Please generate a tactic in lean4 to solve the state.
STATE:
L : Language
M : Type w
inst✝¹ : Nonempty M
inst✝ : Structure L M
T U V : Theory L
x✝ : T ≼ U
h : M ⊧ₘ* U
p : Sentence L
hp : p ∈ T
⊢ inst✝.toStruc ⊧ p
TACTIC:
|
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