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/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [s1] at h2 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply h2 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h1_1 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x h1_y : VarName
V : VarAssignment D
h2 :
β (Q : PredName) (ds ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
V : VarAssignment D
h2 :
β (Q : PredName) (ds : List D),
Q = P... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
V : Var... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1_phi'
h1_ih :
... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1_phi'
h1_ih :
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | congr! 1 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1_phi'
h1_ih :
... | case a.h.e'_1.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h1_ih V h2 | case a.h.e'_1.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_psi h1_phi' h1_psi' : Formula
aβΒΉ : IsSub P zs H h1_phi h1... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_psi h1_phi' h1_psi' : Formula
aβΒΉ : IsSub P zs H h1_phi h1... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | congr! 1 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_psi h1_phi' h1_psi' : Formula
aβΒΉ : IsSub P zs H h1_phi h1... | case a.h.e'_1.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_psi h1_phi' h1_psi' : Formula
aβΒΉ : IsSub ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h1_ih_1 V h2 | case a.h.e'_1.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_psi h1_phi' h1_psi' : Formula
aβΒΉ : IsSub ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h1_ih_2 V h2 | case a.h.e'_2.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_psi h1_phi' h1_psi' : Formula
aβΒΉ : IsSub ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | first | apply forall_congr' | apply exists_congr | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro d | case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x... | case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply h1_ih | case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x... | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro Q ds a1 | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q d... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | specialize h2 Q ds a1 | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q d... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | have s1 :
Holds D I (Function.updateListITE (Function.updateITE V h1_x d) zs ds) E H β
Holds D I (Function.updateListITE V zs ds) E H :=
by
apply Holds_coincide_Var
intro v a1
apply Function.updateListITE_updateIte
intro contra
subst contra
contradiction | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q d... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [h2] at s1 | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q d... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact s1 | case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q d... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply forall_congr' | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply exists_congr | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | case h
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply Holds_coincide_Var | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro v a1 | case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_... | case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply Function.updateListITE_updateIte | case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_... | case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro contra | case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn ... | case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | subst contra | case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn ... | case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1_phi'... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | contradiction | case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1_phi'... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | cases E | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
h2 :
β (Q : Pred... | case nil
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
h2 :
β (Q : Pre... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case nil =>
simp only [Holds] | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
h2 :
β (Q : PredName) (d... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
h2 :
β (Q : PredName) (d... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl : List ... | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl : List ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | split_ifs | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl : List ... | case pos
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
t... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply Holds_coincide_PredVar | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl : List ... | case h1
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h3_const | case h1
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [predVarOccursIn_iff_mem_predVarSet] | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [hd.h2] | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply Holds_coincide_PredVar | D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl : List ... | case h1
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h3_const | case h1
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [predVarOccursIn] | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp | case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : DefName
xs : List VarName
V : VarAssignment D
hd : Definition
tl... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
X : Def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp only [IsValid] at h2 | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : F.IsValid
β’ F'.IsValid | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ F'.IsValid | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : F.IsValid
β’ F'.IsValid
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp only [IsValid] | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ F'.IsValid | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F' | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ F'.IsValid
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | intro D I V E | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F' | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I V E F' | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
β’ β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F'
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | let J : Interpretation D :=
{ nonempty := I.nonempty
pred_const_ := I.pred_const_
pred_var_ := fun (Q : PredName) (ds : List D) =>
if (Q = P β§ ds.length = zs.length)
then Holds D I (Function.updateListITE V zs ds) E H
else I.pred_var_ Q ds } | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I V E F' | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
β’ Holds D I V E F'
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | obtain s1 := substitution_theorem D I J V E F P zs H F' h1 | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp only [Interpretation.pred_var_] at s1 | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp only [s2] | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | apply h2 | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | apply s1 | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | case h2
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_v... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | intro Q ds a1 | case h2
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_v... | case h2
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_v... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | cases a1 | case h2
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_v... | case h2.intro
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | case h2.intro a1_left a1_right =>
simp
simp only [if_pos a1_right] | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp only [if_pos a1_right] | F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := f... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp | case h3_const
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h3_const
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretati... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | intro Q ds a1 | case h3_var
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pr... | case h3_var
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pr... | Please generate a tactic in lean4 to solve the state.
STATE:
case h3_var
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_is_valid | [248, 1] | [282, 11] | simp only [if_neg a1] | case h3_var
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation D :=
{ nonempty := β―, pred_const_ := I.pred_const_,
pr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h3_var
F F' : Formula
P : PredName
zs : List VarName
H : Formula
h1 : IsSub P zs H F F'
h2 : β (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env), Holds D I V E F
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
J : Interpretation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | induction s | Ξ± : Type
s : Str Ξ±
β’ β n, List.reverse s β exp Ξ± n | case nil
Ξ± : Type
β’ β n, [].reverse β exp Ξ± n
case cons
Ξ± : Type
headβ : Ξ±
tailβ : List Ξ±
tail_ihβ : β n, tailβ.reverse β exp Ξ± n
β’ β n, (headβ :: tailβ).reverse β exp Ξ± n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ β n, List.reverse s β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | case nil =>
apply Exists.intro 0
exact exp.zero | Ξ± : Type
β’ β n, [].reverse β exp Ξ± n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
β’ β n, [].reverse β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | case cons hd tl ih =>
apply Exists.elim ih
intro n a1
apply Exists.intro (n + 1)
simp
exact exp.succ n hd tl.reverse a1 | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | apply Exists.intro 0 | Ξ± : Type
β’ β n, [].reverse β exp Ξ± n | Ξ± : Type
β’ [].reverse β exp Ξ± 0 | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
β’ β n, [].reverse β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | exact exp.zero | Ξ± : Type
β’ [].reverse β exp Ξ± 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
β’ [].reverse β exp Ξ± 0
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | apply Exists.elim ih | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β (a : β), tl.reverse β exp Ξ± a β β n, (hd :: tl).reverse β exp Ξ± n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | intro n a1 | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β (a : β), tl.reverse β exp Ξ± a β β n, (hd :: tl).reverse β exp Ξ± n | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
β’ β (a : β), tl.reverse β exp Ξ± a β β n, (hd :: tl).reverse β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | apply Exists.intro (n + 1) | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ (hd :: tl).reverse β exp Ξ± (n + 1) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ β n, (hd :: tl).reverse β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | simp | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ (hd :: tl).reverse β exp Ξ± (n + 1) | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ tl.reverse ++ [hd] β exp Ξ± (n + 1) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ (hd :: tl).reverse β exp Ξ± (n + 1)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp | [53, 1] | [67, 40] | exact exp.succ n hd tl.reverse a1 | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ tl.reverse ++ [hd] β exp Ξ± (n + 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : β n, tl.reverse β exp Ξ± n
n : β
a1 : tl.reverse β exp Ξ± n
β’ tl.reverse ++ [hd] β exp Ξ± (n + 1)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.str_mem_exp | [70, 1] | [77, 13] | obtain s1 := rev_str_mem_exp s.reverse | Ξ± : Type
s : Str Ξ±
β’ β n, s β exp Ξ± n | Ξ± : Type
s : Str Ξ±
s1 : β n, (List.reverse s).reverse β exp Ξ± n
β’ β n, s β exp Ξ± n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ β n, s β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.str_mem_exp | [70, 1] | [77, 13] | simp only [List.reverse_reverse] at s1 | Ξ± : Type
s : Str Ξ±
s1 : β n, (List.reverse s).reverse β exp Ξ± n
β’ β n, s β exp Ξ± n | Ξ± : Type
s : Str Ξ±
s1 : β n, s β exp Ξ± n
β’ β n, s β exp Ξ± n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
s1 : β n, (List.reverse s).reverse β exp Ξ± n
β’ β n, s β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.str_mem_exp | [70, 1] | [77, 13] | exact s1 | Ξ± : Type
s : Str Ξ±
s1 : β n, s β exp Ξ± n
β’ β n, s β exp Ξ± n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
s1 : β n, s β exp Ξ± n
β’ β n, s β exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | induction s | Ξ± : Type
s : Str Ξ±
β’ List.reverse s β exp Ξ± (List.length s) | case nil
Ξ± : Type
β’ [].reverse β exp Ξ± [].length
case cons
Ξ± : Type
headβ : Ξ±
tailβ : List Ξ±
tail_ihβ : tailβ.reverse β exp Ξ± tailβ.length
β’ (headβ :: tailβ).reverse β exp Ξ± (headβ :: tailβ).length | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ List.reverse s β exp Ξ± (List.length s)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | case nil =>
simp
exact exp.zero | Ξ± : Type
β’ [].reverse β exp Ξ± [].length | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
β’ [].reverse β exp Ξ± [].length
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | case cons hd tl ih =>
simp
exact exp.succ tl.length hd tl.reverse ih | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ (hd :: tl).reverse β exp Ξ± (hd :: tl).length | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ (hd :: tl).reverse β exp Ξ± (hd :: tl).length
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | simp | Ξ± : Type
β’ [].reverse β exp Ξ± [].length | Ξ± : Type
β’ [] β exp Ξ± 0 | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
β’ [].reverse β exp Ξ± [].length
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | exact exp.zero | Ξ± : Type
β’ [] β exp Ξ± 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
β’ [] β exp Ξ± 0
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | simp | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ (hd :: tl).reverse β exp Ξ± (hd :: tl).length | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ tl.reverse ++ [hd] β exp Ξ± (tl.length + 1) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ (hd :: tl).reverse β exp Ξ± (hd :: tl).length
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.rev_str_mem_exp_str_len | [80, 1] | [91, 48] | exact exp.succ tl.length hd tl.reverse ih | Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ tl.reverse ++ [hd] β exp Ξ± (tl.length + 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
hd : Ξ±
tl : List Ξ±
ih : tl.reverse β exp Ξ± tl.length
β’ tl.reverse ++ [hd] β exp Ξ± (tl.length + 1)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.str_mem_exp_str_len | [94, 1] | [101, 13] | obtain s1 := rev_str_mem_exp_str_len s.reverse | Ξ± : Type
s : Str Ξ±
β’ s β exp Ξ± (List.length s) | Ξ± : Type
s : Str Ξ±
s1 : (List.reverse s).reverse β exp Ξ± (List.reverse s).length
β’ s β exp Ξ± (List.length s) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ s β exp Ξ± (List.length s)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.str_mem_exp_str_len | [94, 1] | [101, 13] | simp at s1 | Ξ± : Type
s : Str Ξ±
s1 : (List.reverse s).reverse β exp Ξ± (List.reverse s).length
β’ s β exp Ξ± (List.length s) | Ξ± : Type
s : Str Ξ±
s1 : s β exp Ξ± (List.length s)
β’ s β exp Ξ± (List.length s) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
s1 : (List.reverse s).reverse β exp Ξ± (List.reverse s).length
β’ s β exp Ξ± (List.length s)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.str_mem_exp_str_len | [94, 1] | [101, 13] | exact s1 | Ξ± : Type
s : Str Ξ±
s1 : s β exp Ξ± (List.length s)
β’ s β exp Ξ± (List.length s) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
s1 : s β exp Ξ± (List.length s)
β’ s β exp Ξ± (List.length s)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.mem_exp_imp_str_len_eq | [104, 1] | [116, 17] | induction h1 | Ξ± : Type
s : Str Ξ±
n : β
h1 : s β exp Ξ± n
β’ List.length s = n | case zero
Ξ± : Type
s : Str Ξ±
n : β
β’ [].length = 0
case succ
Ξ± : Type
s : Str Ξ±
n nβ : β
aβΒΉ : Ξ±
sβ : Str Ξ±
aβ : sβ β exp Ξ± nβ
a_ihβ : List.length sβ = nβ
β’ List.length (sβ ++ [aβΒΉ]) = nβ + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
n : β
h1 : s β exp Ξ± n
β’ List.length s = n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.mem_exp_imp_str_len_eq | [104, 1] | [116, 17] | case zero =>
simp | Ξ± : Type
s : Str Ξ±
n : β
β’ [].length = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
n : β
β’ [].length = 0
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.mem_exp_imp_str_len_eq | [104, 1] | [116, 17] | case succ m a s ih_1 ih_2 =>
simp
exact ih_2 | Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length (s ++ [a]) = m + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length (s ++ [a]) = m + 1
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.mem_exp_imp_str_len_eq | [104, 1] | [116, 17] | simp | Ξ± : Type
s : Str Ξ±
n : β
β’ [].length = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
n : β
β’ [].length = 0
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.mem_exp_imp_str_len_eq | [104, 1] | [116, 17] | simp | Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length (s ++ [a]) = m + 1 | Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length s = m | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length (s ++ [a]) = m + 1
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.mem_exp_imp_str_len_eq | [104, 1] | [116, 17] | exact ih_2 | Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length s = m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
sβ : Str Ξ±
n m : β
a : Ξ±
s : Str Ξ±
ih_1 : s β exp Ξ± m
ih_2 : List.length s = m
β’ List.length s = m
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.all_str_mem_kleene_closure | [153, 1] | [160, 24] | simp only [kleene_closure] | Ξ± : Type
s : Str Ξ±
β’ s β kleene_closure Ξ± | Ξ± : Type
s : Str Ξ±
β’ s β β n, exp Ξ± n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ s β kleene_closure Ξ±
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.all_str_mem_kleene_closure | [153, 1] | [160, 24] | simp | Ξ± : Type
s : Str Ξ±
β’ s β β n, exp Ξ± n | Ξ± : Type
s : Str Ξ±
β’ β i, s β exp Ξ± i | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ s β β n, exp Ξ± n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.all_str_mem_kleene_closure | [153, 1] | [160, 24] | exact str_mem_exp s | Ξ± : Type
s : Str Ξ±
β’ β i, s β exp Ξ± i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s : Str Ξ±
β’ β i, s β exp Ξ± i
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.thm_2 | [192, 1] | [198, 36] | symm | Ξ± : Type
s t u : Str Ξ±
β’ s ++ (t ++ u) = s ++ t ++ u | Ξ± : Type
s t u : Str Ξ±
β’ s ++ t ++ u = s ++ (t ++ u) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s t u : Str Ξ±
β’ s ++ (t ++ u) = s ++ t ++ u
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Strings.thm_2 | [192, 1] | [198, 36] | exact (List.append_assoc s t u) | Ξ± : Type
s t u : Str Ξ±
β’ s ++ t ++ u = s ++ (t ++ u) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
s t u : Str Ξ±
β’ s ++ t ++ u = s ++ (t ++ u)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_a | [237, 1] | [243, 9] | simp only [concat] | Ξ± : Type
L : Language Ξ±
β’ concat L β
= β
| Ξ± : Type
L : Language Ξ±
β’ {x | β s β L, β t β β
, s ++ t = x} = β
| Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ concat L β
= β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_a | [237, 1] | [243, 9] | simp | Ξ± : Type
L : Language Ξ±
β’ {x | β s β L, β t β β
, s ++ t = x} = β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ {x | β s β L, β t β β
, s ++ t = x} = β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_b | [246, 1] | [252, 9] | simp only [concat] | Ξ± : Type
L : Language Ξ±
β’ concat β
L = β
| Ξ± : Type
L : Language Ξ±
β’ {x | β s β β
, β t β L, s ++ t = x} = β
| Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ concat β
L = β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_b | [246, 1] | [252, 9] | simp | Ξ± : Type
L : Language Ξ±
β’ {x | β s β β
, β t β L, s ++ t = x} = β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ {x | β s β β
, β t β L, s ++ t = x} = β
TACTIC:
|
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