url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
| input
stringlengths 73
2.09M
|
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
exact h1
|
case refine'_1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (forall_ v P.not_).not_
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (forall_ v P.not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
intro contra
|
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ ¬isFreeIn t Q
|
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ False
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ ¬isFreeIn t Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply h4
|
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ False
|
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ occursIn t Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ False
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply isFreeIn_imp_occursIn
|
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ occursIn t Q
|
case refine'_2.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ isFreeIn t Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ occursIn t Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
exact contra
|
case refine'_2.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ isFreeIn t Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
contra : isFreeIn t Q
⊢ isFreeIn t Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
⊢ IsProof ((exists_ v (P.and_ Q)).imp_ ((exists_ v P).and_ (exists_ v Q)))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {exists_ v (P.and_ Q)}) ((exists_ v P).and_ (exists_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((exists_ v (P.and_ Q)).imp_ ((exists_ v P).and_ (exists_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {exists_ v (P.and_ Q)}) ((exists_ v P).and_ (exists_ v Q))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} ((exists_ v P).and_ (exists_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {exists_ v (P.and_ Q)}) ((exists_ v P).and_ (exists_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply rule_C (P.and_ Q) ((exists_ v P).and_ (exists_ v Q)) v
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} ((exists_ v P).and_ (exists_ v Q))
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} (exists_ v (P.and_ Q))
case h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v P).and_ (exists_ v Q))
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.and_ Q)}, ¬isFreeIn v H
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).and_ (exists_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} ((exists_ v P).and_ (exists_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.assume_
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} (exists_ v (P.and_ Q))
|
case h1.h1.a
P Q : Formula
v : VarName
⊢ exists_ v (P.and_ Q) ∈ {exists_ v (P.and_ Q)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} (exists_ v (P.and_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1.h1.a
P Q : Formula
v : VarName
⊢ exists_ v (P.and_ Q) ∈ {exists_ v (P.and_ Q)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a
P Q : Formula
v : VarName
⊢ exists_ v (P.and_ Q) ∈ {exists_ v (P.and_ Q)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.mp_ (exists_ v Q)
|
case h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v P).and_ (exists_ v Q))
|
case h1.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v Q).imp_ ((exists_ v P).and_ (exists_ v Q)))
case h1.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (exists_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v P).and_ (exists_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.mp_ (exists_ v P)
|
case h1.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v Q).imp_ ((exists_ v P).and_ (exists_ v Q)))
|
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q})
((exists_ v P).imp_ ((exists_ v Q).imp_ ((exists_ v P).and_ (exists_ v Q))))
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (exists_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v Q).imp_ ((exists_ v P).and_ (exists_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_and_]
|
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q})
((exists_ v P).imp_ ((exists_ v Q).imp_ ((exists_ v P).and_ (exists_ v Q))))
|
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_})
((exists_ v P).imp_ ((exists_ v Q).imp_ ((exists_ v P).imp_ (exists_ v Q).not_).not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q})
((exists_ v P).imp_ ((exists_ v Q).imp_ ((exists_ v P).and_ (exists_ v Q))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
SC
|
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_})
((exists_ v P).imp_ ((exists_ v Q).imp_ ((exists_ v P).imp_ (exists_ v Q).not_).not_))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_})
((exists_ v P).imp_ ((exists_ v Q).imp_ ((exists_ v P).imp_ (exists_ v Q).not_).not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply exists_intro P v v
|
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (exists_ v P)
|
case h1.h2.a.a.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v P
case h1.h2.a.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (fastReplaceFree v v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (exists_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply fastAdmits_self
|
case h1.h2.a.a.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [fastReplaceFree_self]
|
case h1.h2.a.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (fastReplaceFree v v P)
|
case h1.h2.a.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (fastReplaceFree v v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.mp_ (P.and_ Q)
|
case h1.h2.a.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) P
|
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((P.and_ Q).imp_ P)
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (P.and_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_and_]
|
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((P.and_ Q).imp_ P)
|
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_}) ((P.imp_ Q.not_).not_.imp_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((P.and_ Q).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
SC
|
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_}) ((P.imp_ Q.not_).not_.imp_ P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_}) ((P.imp_ Q.not_).not_.imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.assume_
|
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (P.and_ Q)
|
case h1.h2.a.a.h2.a.a
P Q : Formula
v : VarName
⊢ P.and_ Q ∈ {exists_ v (P.and_ Q)} ∪ {P.and_ Q}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (P.and_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1.h2.a.a.h2.a.a
P Q : Formula
v : VarName
⊢ P.and_ Q ∈ {exists_ v (P.and_ Q)} ∪ {P.and_ Q}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.a.h2.a.a
P Q : Formula
v : VarName
⊢ P.and_ Q ∈ {exists_ v (P.and_ Q)} ∪ {P.and_ Q}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply exists_intro Q v v
|
case h1.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (exists_ v Q)
|
case h1.h2.a.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v Q
case h1.h2.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (fastReplaceFree v v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (exists_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply fastAdmits_self
|
case h1.h2.a.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [fastReplaceFree_self]
|
case h1.h2.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (fastReplaceFree v v Q)
|
case h1.h2.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (fastReplaceFree v v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.mp_ (P.and_ Q)
|
case h1.h2.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) Q
|
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((P.and_ Q).imp_ Q)
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (P.and_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_and_]
|
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((P.and_ Q).imp_ Q)
|
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_}) ((P.imp_ Q.not_).not_.imp_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((P.and_ Q).imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
SC
|
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_}) ((P.imp_ Q.not_).not_.imp_ Q)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.imp_ Q.not_).not_} ∪ {(P.imp_ Q.not_).not_}) ((P.imp_ Q.not_).not_.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
apply IsDeduct.assume_
|
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (P.and_ Q)
|
case h1.h2.a.h2.a.a
P Q : Formula
v : VarName
⊢ P.and_ Q ∈ {exists_ v (P.and_ Q)} ∪ {P.and_ Q}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) (P.and_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1.h2.a.h2.a.a
P Q : Formula
v : VarName
⊢ P.and_ Q ∈ {exists_ v (P.and_ Q)} ∪ {P.and_ Q}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2.a.h2.a.a
P Q : Formula
v : VarName
⊢ P.and_ Q ∈ {exists_ v (P.and_ Q)} ∪ {P.and_ Q}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_and_]
|
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.and_ Q)}, ¬isFreeIn v H
|
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.imp_ Q.not_).not_}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.and_ Q)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_exists_]
|
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.imp_ Q.not_).not_}, ¬isFreeIn v H
|
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {(forall_ v (P.imp_ Q.not_).not_.not_).not_}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.imp_ Q.not_).not_}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {(forall_ v (P.imp_ Q.not_).not_.not_).not_}, ¬isFreeIn v H
|
case h1.h3
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v (P.imp_ Q.not_).not_.not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {(forall_ v (P.imp_ Q.not_).not_.not_).not_}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [isFreeIn]
|
case h1.h3
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v (P.imp_ Q.not_).not_.not_).not_
|
case h1.h3
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h3
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v (P.imp_ Q.not_).not_.not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1.h3
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h3
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_and_]
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).and_ (exists_ v Q))
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).imp_ (exists_ v Q).not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).and_ (exists_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [def_exists_]
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).imp_ (exists_ v Q).not_).not_
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_.not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).imp_ (exists_ v Q).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp only [isFreeIn]
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_.not_).not_
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P ∨ ¬True ∧ isFreeIn v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_.not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_14
|
[606, 1]
|
[651, 9]
|
simp
|
case h1.h4
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P ∨ ¬True ∧ isFreeIn v Q)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h4
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P ∨ ¬True ∧ isFreeIn v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp only [def_iff_]
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v P).imp_ (forall_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply deduction_theorem
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v P).imp_ (forall_ v Q))
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v P}) (forall_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v P).imp_ (forall_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v P}) (forall_ v Q)
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v P}) (forall_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply generalization
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
|
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply IsDeduct.mp_ P
|
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (P.imp_ Q)
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply IsDeduct.mp_ ((P.imp_ Q).and_ (Q.imp_ P))
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (P.imp_ Q)
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (P.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp only [def_and_]
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
SC
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.imp_ Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply specId v
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
|
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp
|
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply specId v
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
|
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
|
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v P ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp
|
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v P ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v P ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp only [isFreeIn]
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_left
|
[654, 1]
|
[678, 9]
|
simp
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp only [def_iff_]
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)))
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P)))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v Q).imp_ (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply deduction_theorem
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v Q).imp_ (forall_ v P))
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v Q}) (forall_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v Q).imp_ (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v Q}) (forall_ v P)
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v Q}) (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply generalization
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
|
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply IsDeduct.mp_ Q
|
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (Q.imp_ P)
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply IsDeduct.mp_ ((P.imp_ Q).and_ (Q.imp_ P))
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (Q.imp_ P)
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (Q.imp_ P))
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (Q.imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp only [def_and_]
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (Q.imp_ P))
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (Q.imp_ P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
SC
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (Q.imp_ P))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply specId v
|
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
|
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp
|
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply specId v
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
|
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
|
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v Q ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp
|
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v Q ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v Q ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp only [isFreeIn]
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1_right
|
[681, 1]
|
[705, 9]
|
simp
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)))
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
|
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))))
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))))
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))))
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
simp only [def_iff_]
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))))
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ (forall_ v P))))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
simp only [def_and_]
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ (forall_ v P))))))
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P).imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)).not_).not_)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ (forall_ v P))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
SC
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P).imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)).not_).not_)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P).imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)).not_).not_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
apply T_18_1_left
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_1
|
[708, 1]
|
[721, 23]
|
apply T_18_1_right
|
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
induction xs
|
xs : List VarName
P : Formula
⊢ IsProof ((Forall_ xs P).imp_ P)
|
case nil
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
case cons
P : Formula
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : IsProof ((Forall_ tail✝ P).imp_ P)
⊢ IsProof ((Forall_ (head✝ :: tail✝) P).imp_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
xs : List VarName
P : Formula
⊢ IsProof ((Forall_ xs P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
case nil =>
simp only [Forall_]
apply prop_id
|
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
case cons xs_hd xs_tl xs_ih =>
simp only [Forall_]
apply deduction_theorem
simp
apply IsDeduct.mp_ (Forall_ xs_tl P)
apply proof_imp_deduct
exact xs_ih
apply specId xs_hd
apply IsDeduct.assume_
simp
rfl
|
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
simp only [Forall_]
|
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
|
P : Formula
⊢ IsProof ((List.foldr forall_ P []).imp_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
apply prop_id
|
P : Formula
⊢ IsProof ((List.foldr forall_ P []).imp_ P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof ((List.foldr forall_ P []).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
simp only [Forall_]
|
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P)
|
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((List.foldr forall_ P (xs_hd :: xs_tl)).imp_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
apply deduction_theorem
|
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((List.foldr forall_ P (xs_hd :: xs_tl)).imp_ P)
|
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct (∅ ∪ {List.foldr forall_ P (xs_hd :: xs_tl)}) P
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((List.foldr forall_ P (xs_hd :: xs_tl)).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
simp
|
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct (∅ ∪ {List.foldr forall_ P (xs_hd :: xs_tl)}) P
|
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct (∅ ∪ {List.foldr forall_ P (xs_hd :: xs_tl)}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
apply IsDeduct.mp_ (Forall_ xs_tl P)
|
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} P
|
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
apply proof_imp_deduct
|
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
|
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
exact xs_ih
|
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
|
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
apply specId xs_hd
|
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
|
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (forall_ xs_hd (Forall_ xs_tl P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
apply IsDeduct.assume_
|
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (forall_ xs_hd (Forall_ xs_tl P))
|
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ forall_ xs_hd (Forall_ xs_tl P) ∈ {forall_ xs_hd (List.foldr forall_ P xs_tl)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (forall_ xs_hd (Forall_ xs_tl P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
simp
|
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ forall_ xs_hd (Forall_ xs_tl P) ∈ {forall_ xs_hd (List.foldr forall_ P xs_tl)}
|
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ Forall_ xs_tl P = List.foldr forall_ P xs_tl
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ forall_ xs_hd (Forall_ xs_tl P) ∈ {forall_ xs_hd (List.foldr forall_ P xs_tl)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id
|
[724, 1]
|
[743, 8]
|
rfl
|
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ Forall_ xs_tl P = List.foldr forall_ P xs_tl
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ Forall_ xs_tl P = List.foldr forall_ P xs_tl
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id'
|
[746, 1]
|
[764, 13]
|
induction xs
|
xs : List VarName
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ xs P)
⊢ IsDeduct Δ P
|
case nil
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P
case cons
P : Formula
Δ : Set Formula
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : IsDeduct Δ (Forall_ tail✝ P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (head✝ :: tail✝) P)
⊢ IsDeduct Δ P
|
Please generate a tactic in lean4 to solve the state.
STATE:
xs : List VarName
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ xs P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id'
|
[746, 1]
|
[764, 13]
|
case nil =>
simp only [Forall_] at h1
simp at h1
exact h1
|
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.Forall_spec_id'
|
[746, 1]
|
[764, 13]
|
case cons xs_hd xs_tl xs_ih =>
simp only [Forall_] at h1
simp at h1
apply xs_ih
simp only [Forall_]
apply specId xs_hd
exact h1
|
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P)
⊢ IsDeduct Δ P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P)
⊢ IsDeduct Δ P
TACTIC:
|
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