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 |
|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ Holds D I V E h1_phi.not_ ↔ Holds D I V E h1_phi'.not_ | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ ¬Holds D I V E h1_phi ↔ ¬Holds D I V E h1_phi' |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | congr! 1 | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ ¬Holds D I V E h1_phi ↔ ¬Holds D I V E h1_phi' | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ Holds D I V E h1_phi ↔ Holds D I V E h1_phi' |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih V | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ Holds D I V E h1_phi ↔ Holds D I V E h1_phi' | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_psi h1_psi' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_psi h1_psi'
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_psi ↔ Holds D I V E h1_psi'
V : VarAssignment ... | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_psi h1_psi' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_psi h1_psi'
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_psi ↔ Holds D I V E h1_psi'
V : VarAssignment ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | congr! 1 | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_psi h1_psi' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_psi h1_psi'
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_psi ↔ Holds D I V E h1_psi'
V : VarAssignment ... | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_psi h1_psi' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_psi h1_psi'
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_psi ↔ Holds D I V E h1_psi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih_1 V | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_psi h1_psi' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_psi h1_psi'
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_psi ↔ Holds D I V E h1_psi'
V ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih_2 V | case a.h.e'_2.a
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_psi h1_psi' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_psi h1_psi'
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_psi ↔ Holds D I V E h1_psi'
V ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ Holds D I V E (exists_ h1_x h1_phi) ↔ Holds D I V E (exists_ h1_x h1_psi) | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ (∃ d, Holds D I (Function.updateITE V h1_x d) E h1_phi) ↔ ∃ d, Holds D I (Function.updateITE V h1_x d) E h1_psi |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | first | apply forall_congr' | apply exists_congr | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ (∃ d, Holds D I (Function.updateITE V h1_x d) E h1_phi) ↔ ∃ d, Holds D I (Function.updateITE V h1_x d) E h1_psi | case h
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ ∀ (a : D), Holds D I (Function.updateITE V h1_x a) E h1_phi ↔ Holds D I (Function.updateITE V h1_x a) E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | intro d | case h
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ ∀ (a : D), Holds D I (Function.updateITE V h1_x a) E h1_phi ↔ Holds D I (Function.updateITE V h1_x a) E ... | case h
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
d : D
⊢ Holds D I (Function.updateITE V h1_x d) E h1_phi ↔ Holds D I (Function.updateITE V h1_x d) E h1_ps... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih (Function.updateITE V h1_x d) | case h
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
d : D
⊢ Holds D I (Function.updateITE V h1_x d) E h1_phi ↔ Holds D I (Function.updateITE V h1_x d) E h1_ps... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | apply forall_congr' | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ (∀ (d : D), Holds D I (Function.updateITE V h1_x d) E h1_phi) ↔
∀ (d : D), Holds D I (Function.updateITE V ... | case h
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ ∀ (a : D), Holds D I (Function.updateITE V h1_x a) E h1_phi ↔ Holds D I (Function.updateITE V h1_x a) E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | apply exists_congr | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ (∃ d, Holds D I (Function.updateITE V h1_x d) E h1_phi) ↔ ∃ d, Holds D I (Function.updateITE V h1_x d) E h1_psi | case h
D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_psi : Formula
h1_x : VarName
a✝ : AlphaEqv h1_phi h1_psi
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_psi
V : VarAssignment D
⊢ ∀ (a : D), Holds D I (Function.updateITE V h1_x a) E h1_phi ↔ Holds D I (Function.updateITE V h1_x a) E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | rfl | D : Type
I : Interpretation D
E : Env
F F' h1 : Formula
V : VarAssignment D
⊢ Holds D I V E h1 ↔ Holds D I V E h1 | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | symm | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ Holds D I V E h1_phi' ↔ Holds D I V E h1_phi | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ Holds D I V E h1_phi ↔ Holds D I V E h1_phi' |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih V | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' : Formula
a✝ : AlphaEqv h1_phi h1_phi'
h1_ih : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
V : VarAssignment D
⊢ Holds D I V E h1_phi ↔ Holds D I V E h1_phi' | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | trans Holds D I V E h1_phi' | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_phi'' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_phi' h1_phi''
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_phi' ↔ Holds D I V E h1_phi''
V : VarAssignment D
... | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_phi'' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_phi' h1_phi''
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_phi' ↔ Holds D I V E h1_phi''
V : VarAssignment D
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih_1 V | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_phi'' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_phi' h1_phi''
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_phi' ↔ Holds D I V E h1_phi''
V : VarAssignment D
... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.Holds_iff_alphaEqv_Holds | [348, 1] | [389, 22] | exact h1_ih_2 V | D : Type
I : Interpretation D
E : Env
F F' h1_phi h1_phi' h1_phi'' : Formula
a✝¹ : AlphaEqv h1_phi h1_phi'
a✝ : AlphaEqv h1_phi' h1_phi''
h1_ih_1 : ∀ (V : VarAssignment D), Holds D I V E h1_phi ↔ Holds D I V E h1_phi'
h1_ih_2 : ∀ (V : VarAssignment D), Holds D I V E h1_phi' ↔ Holds D I V E h1_phi''
V : VarAssignment D
... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | induction xs | xs : List VarName
⊢ isAlphaEqvVarList [] xs xs | case nil
⊢ isAlphaEqvVarList [] [] []
case cons
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : isAlphaEqvVarList [] tail✝ tail✝
⊢ isAlphaEqvVarList [] (head✝ :: tail✝) (head✝ :: tail✝) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | case nil =>
simp only [isAlphaEqvVarList] | ⊢ isAlphaEqvVarList [] [] [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | simp only [isAlphaEqvVarList] | ⊢ isAlphaEqvVarList [] [] [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | simp only [isAlphaEqvVarList] | hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVarList [] (hd :: tl) (hd :: tl) | hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVar [] hd hd ∧ isAlphaEqvVarList [] tl tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | constructor | hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVar [] hd hd ∧ isAlphaEqvVarList [] tl tl | case left
hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVar [] hd hd
case right
hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVarList [] tl tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | simp only [isAlphaEqvVar] | case left
hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVar [] hd hd | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarListId | [441, 1] | [452, 15] | exact ih | case right
hd : VarName
tl : List VarName
ih : isAlphaEqvVarList [] tl tl
⊢ isAlphaEqvVarList [] tl tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | induction h1 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvVar binders x y
⊢ V x = V' y | case nil
D : Type
binders : List (VarName × VarName)
x y : VarName
V V' V✝ : VarAssignment D
h2 : isAlphaEqvVar [] x y
⊢ V✝ x = V✝ y
case cons
D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
binders✝ : List (VarName × VarName)
x✝ y✝ : VarName
V✝ V'✝ : VarAssignment D
d✝ : D
a✝ : AlphaE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case nil h1_V =>
simp only [isAlphaEqvVar] at h2
subst h2
rfl | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' h1_V : VarAssignment D
h2 : isAlphaEqvVar [] x y
⊢ h1_V x = h1_V y | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case cons h1_l h1_x h1_y h1_V h1_V' h1_d _ h1_ih =>
simp only [isAlphaEqvVar] at h2
simp only [Function.updateITE]
cases h2
case inl h2 =>
cases h2
case intro h2_left h2_right =>
simp only [if_pos h2_left, if_pos h2_right]
case inr h2 =>
cases h2
case intro h2_left h2_right =>
case... | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : isAlphaEqvVar ((h1_x, h1_y) :: h1_l) x y
⊢ Functi... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | simp only [isAlphaEqvVar] at h2 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' h1_V : VarAssignment D
h2 : isAlphaEqvVar [] x y
⊢ h1_V x = h1_V y | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' h1_V : VarAssignment D
h2 : x = y
⊢ h1_V x = h1_V y |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | subst h2 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' h1_V : VarAssignment D
h2 : x = y
⊢ h1_V x = h1_V y | D : Type
binders : List (VarName × VarName)
x : VarName
V V' h1_V : VarAssignment D
⊢ h1_V x = h1_V x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | rfl | D : Type
binders : List (VarName × VarName)
x : VarName
V V' h1_V : VarAssignment D
⊢ h1_V x = h1_V x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | simp only [isAlphaEqvVar] at h2 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : isAlphaEqvVar ((h1_x, h1_y) :: h1_l) x y
⊢ Functi... | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : x = h1_x ∧ y = h1_y ∨ (¬x = h1_x ∧ ¬y = h1_y) ∧ i... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | simp only [Function.updateITE] | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : x = h1_x ∧ y = h1_y ∨ (¬x = h1_x ∧ ¬y = h1_y) ∧ i... | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : x = h1_x ∧ y = h1_y ∨ (¬x = h1_x ∧ ¬y = h1_y) ∧ i... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | cases h2 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : x = h1_x ∧ y = h1_y ∨ (¬x = h1_x ∧ ¬y = h1_y) ∧ i... | case inl
D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h✝ : x = h1_x ∧ y = h1_y
⊢ (if x = h1_x then ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case inl h2 =>
cases h2
case intro h2_left h2_right =>
simp only [if_pos h2_left, if_pos h2_right] | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : x = h1_x ∧ y = h1_y
⊢ (if x = h1_x then h1_d else... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case inr h2 =>
cases h2
case intro h2_left h2_right =>
cases h2_left
case intro h2_left_left h2_left_right =>
simp only [if_neg h2_left_left, if_neg h2_left_right]
exact h1_ih h2_right | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : (¬x = h1_x ∧ ¬y = h1_y) ∧ isAlphaEqvVar h1_l x y
... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | cases h2 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : x = h1_x ∧ y = h1_y
⊢ (if x = h1_x then h1_d else... | case intro
D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
left✝ : x = h1_x
right✝ : y = h1_y
⊢ (if x ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case intro h2_left h2_right =>
simp only [if_pos h2_left, if_pos h2_right] | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_left : x = h1_x
h2_right : y = h1_y
⊢ (if x = h1_x ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | simp only [if_pos h2_left, if_pos h2_right] | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_left : x = h1_x
h2_right : y = h1_y
⊢ (if x = h1_x ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | cases h2 | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2 : (¬x = h1_x ∧ ¬y = h1_y) ∧ isAlphaEqvVar h1_l x y
... | case intro
D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
left✝ : ¬x = h1_x ∧ ¬y = h1_y
right✝ : isAl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case intro h2_left h2_right =>
cases h2_left
case intro h2_left_left h2_left_right =>
simp only [if_neg h2_left_left, if_neg h2_left_right]
exact h1_ih h2_right | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_left : ¬x = h1_x ∧ ¬y = h1_y
h2_right : isAlphaEqvV... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | cases h2_left | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_left : ¬x = h1_x ∧ ¬y = h1_y
h2_right : isAlphaEqvV... | case intro
D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_right : isAlphaEqvVar h1_l x y
left✝ : ¬... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | case intro h2_left_left h2_left_right =>
simp only [if_neg h2_left_left, if_neg h2_left_right]
exact h1_ih h2_right | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_right : isAlphaEqvVar h1_l x y
h2_left_left : ¬x = ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | simp only [if_neg h2_left_left, if_neg h2_left_right] | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_right : isAlphaEqvVar h1_l x y
h2_left_left : ¬x = ... | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_right : isAlphaEqvVar h1_l x y
h2_left_left : ¬x = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_1 | [531, 1] | [561, 31] | exact h1_ih h2_right | D : Type
binders : List (VarName × VarName)
x y : VarName
V V' : VarAssignment D
h1_l : List (VarName × VarName)
h1_x h1_y : VarName
h1_V h1_V' : VarAssignment D
h1_d : D
a✝ : AlphaEqvVarAssignment D h1_l h1_V h1_V'
h1_ih : isAlphaEqvVar h1_l x y → h1_V x = h1_V' y
h2_right : isAlphaEqvVar h1_l x y
h2_left_left : ¬x = ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | induction xs generalizing ys | D : Type
binders : List (VarName × VarName)
xs ys : List VarName
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvVarList binders xs ys
⊢ List.map V xs = List.map V' ys | case nil
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
ys : List VarName
h2 : isAlphaEqvVarList binders [] ys
⊢ List.map V [] = List.map V' ys
case cons
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | case nil =>
cases ys
case nil =>
simp
case cons ys_hd ys_tl =>
simp only [isAlphaEqvVarList] at h2 | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
ys : List VarName
h2 : isAlphaEqvVarList binders [] ys
⊢ List.map V [] = List.map V' ys | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | cases ys | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
ys : List VarName
h2 : isAlphaEqvVarList binders [] ys
⊢ List.map V [] = List.map V' ys | case nil
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvVarList binders [] []
⊢ List.map V [] = List.map V' []
case cons
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
head✝ : VarN... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | case nil =>
simp | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvVarList binders [] []
⊢ List.map V [] = List.map V' [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | case cons ys_hd ys_tl =>
simp only [isAlphaEqvVarList] at h2 | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVarList binders [] (ys_hd :: ys_tl)
⊢ List.map V [] = List.map V' (ys_hd :: ys_tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | simp | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvVarList binders [] []
⊢ List.map V [] = List.map V' [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | simp only [isAlphaEqvVarList] at h2 | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVarList binders [] (ys_hd :: ys_tl)
⊢ List.map V [] = List.map V' (ys_hd :: ys_tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | cases ys | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys : List VarName
h2 : isAlphaEqvVarList binders (xs_hd :: xs_tl) ys
⊢ L... | case nil
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
h2 : isAlphaEqvVarList binders (xs_hd :: xs_tl) []
⊢ List.map V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | case nil =>
simp only [isAlphaEqvVarList] at h2 | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
h2 : isAlphaEqvVarList binders (xs_hd :: xs_tl) []
⊢ List.map V (xs_hd :... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | simp only [isAlphaEqvVarList] at h2 | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
h2 : isAlphaEqvVarList binders (xs_hd :: xs_tl) []
⊢ List.map V (xs_hd :... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | simp only [isAlphaEqvVarList] at h2 | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVarList binders (xs_... | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binders xs_hd ys... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | simp | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binders xs_hd ys... | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binders xs_hd ys... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | constructor | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binders xs_hd ys... | case left
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binder... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | cases h2 | case left
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binder... | case left.intro
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
left✝ : isAlphaEqvV... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | case left.intro h2_left h2_right =>
exact aux_1 D binders xs_hd ys_hd V V' h1 h2_left | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2_left : isAlphaEqvVar binders xs_... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | exact aux_1 D binders xs_hd ys_hd V V' h1 h2_left | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2_left : isAlphaEqvVar binders xs_... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | apply xs_ih ys_tl | case right
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binde... | case right
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | cases h2 | case right
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2 : isAlphaEqvVar binde... | case right.intro
D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
left✝ : isAlphaEqv... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | case right.intro h2_left h2_right =>
exact h2_right | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2_left : isAlphaEqvVar binders xs_... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.aux_2 | [564, 1] | [595, 25] | exact h2_right | D : Type
binders : List (VarName × VarName)
V V' : VarAssignment D
h1 : AlphaEqvVarAssignment D binders V V'
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → List.map V xs_tl = List.map V' ys
ys_hd : VarName
ys_tl : List VarName
h2_left : isAlphaEqvVar binders xs_... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | induction xs generalizing ys | binders : List (VarName × VarName)
xs ys : List VarName
h1 : isAlphaEqvVarList binders xs ys
⊢ xs.length = ys.length | case nil
binders : List (VarName × VarName)
ys : List VarName
h1 : isAlphaEqvVarList binders [] ys
⊢ [].length = ys.length
case cons
binders : List (VarName × VarName)
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : ∀ (ys : List VarName), isAlphaEqvVarList binders tail✝ ys → tail✝.length = ys.length
ys : List VarName
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case nil =>
cases ys
case nil =>
rfl
case cons ys_hd ys_tl =>
simp only [isAlphaEqvVarList] at h1 | binders : List (VarName × VarName)
ys : List VarName
h1 : isAlphaEqvVarList binders [] ys
⊢ [].length = ys.length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case cons xs_hd xs_tl xs_ih =>
cases ys
case nil =>
simp only [isAlphaEqvVarList] at h1
case cons ys_hd ys_tl =>
simp only [isAlphaEqvVarList] at h1
simp
cases h1
case intro h1_left h1_right =>
exact xs_ih ys_tl h1_right | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys : List VarName
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) ys
⊢ (xs_hd :: xs_tl).length = ys.length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | cases ys | binders : List (VarName × VarName)
ys : List VarName
h1 : isAlphaEqvVarList binders [] ys
⊢ [].length = ys.length | case nil
binders : List (VarName × VarName)
h1 : isAlphaEqvVarList binders [] []
⊢ [].length = [].length
case cons
binders : List (VarName × VarName)
head✝ : VarName
tail✝ : List VarName
h1 : isAlphaEqvVarList binders [] (head✝ :: tail✝)
⊢ [].length = (head✝ :: tail✝).length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case nil =>
rfl | binders : List (VarName × VarName)
h1 : isAlphaEqvVarList binders [] []
⊢ [].length = [].length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case cons ys_hd ys_tl =>
simp only [isAlphaEqvVarList] at h1 | binders : List (VarName × VarName)
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVarList binders [] (ys_hd :: ys_tl)
⊢ [].length = (ys_hd :: ys_tl).length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | rfl | binders : List (VarName × VarName)
h1 : isAlphaEqvVarList binders [] []
⊢ [].length = [].length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | simp only [isAlphaEqvVarList] at h1 | binders : List (VarName × VarName)
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVarList binders [] (ys_hd :: ys_tl)
⊢ [].length = (ys_hd :: ys_tl).length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | cases ys | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys : List VarName
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) ys
⊢ (xs_hd :: xs_tl).length = ys.length | case nil
binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) []
⊢ (xs_hd :: xs_tl).length = [].length
case cons
binders : List (VarName × VarName)
xs_hd : Var... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case nil =>
simp only [isAlphaEqvVarList] at h1 | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) []
⊢ (xs_hd :: xs_tl).length = [].length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case cons ys_hd ys_tl =>
simp only [isAlphaEqvVarList] at h1
simp
cases h1
case intro h1_left h1_right =>
exact xs_ih ys_tl h1_right | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) (ys_hd :: ys_tl)
⊢ (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | simp only [isAlphaEqvVarList] at h1 | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) []
⊢ (xs_hd :: xs_tl).length = [].length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | simp only [isAlphaEqvVarList] at h1 | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVarList binders (xs_hd :: xs_tl) (ys_hd :: ys_tl)
⊢ (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVar binders xs_hd ys_hd ∧ isAlphaEqvVarList binders xs_tl ys_tl
⊢ (xs_hd :: xs_tl).length = (ys_hd :: y... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | simp | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVar binders xs_hd ys_hd ∧ isAlphaEqvVarList binders xs_tl ys_tl
⊢ (xs_hd :: xs_tl).length = (ys_hd :: y... | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVar binders xs_hd ys_hd ∧ isAlphaEqvVarList binders xs_tl ys_tl
⊢ xs_tl.length = ys_tl.length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | cases h1 | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1 : isAlphaEqvVar binders xs_hd ys_hd ∧ isAlphaEqvVarList binders xs_tl ys_tl
⊢ xs_tl.length = ys_tl.length | case intro
binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
left✝ : isAlphaEqvVar binders xs_hd ys_hd
right✝ : isAlphaEqvVarList binders xs_tl ys_tl
⊢ xs_tl.length = y... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | case intro h1_left h1_right =>
exact xs_ih ys_tl h1_right | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1_left : isAlphaEqvVar binders xs_hd ys_hd
h1_right : isAlphaEqvVarList binders xs_tl ys_tl
⊢ xs_tl.length = ys_tl.le... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqvVarList_length | [598, 1] | [621, 35] | exact xs_ih ys_tl h1_right | binders : List (VarName × VarName)
xs_hd : VarName
xs_tl : List VarName
xs_ih : ∀ (ys : List VarName), isAlphaEqvVarList binders xs_tl ys → xs_tl.length = ys.length
ys_hd : VarName
ys_tl : List VarName
h1_left : isAlphaEqvVar binders xs_hd ys_hd
h1_right : isAlphaEqvVarList binders xs_tl ys_tl
⊢ xs_tl.length = ys_tl.le... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | induction E generalizing F F' binders V V' | D : Type
I : Interpretation D
V V' : VarAssignment D
E : Env
F F' : Formula
binders : List (VarName × VarName)
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvAux binders F F'
⊢ Holds D I V E F ↔ Holds D I V' E F' | case nil
D : Type
I : Interpretation D
V V' : VarAssignment D
F F' : Formula
binders : List (VarName × VarName)
h1 : AlphaEqvVarAssignment D binders V V'
h2 : isAlphaEqvAux binders F F'
⊢ Holds D I V [] F ↔ Holds D I V' [] F'
case cons
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | case nil.def_.def_ =>
simp only [Holds] | D : Type
I : Interpretation D
a✝³ : DefName
a✝² : List VarName
V V' : VarAssignment D
binders : List (VarName × VarName)
h1 : AlphaEqvVarAssignment D binders V V'
a✝¹ : DefName
a✝ : List VarName
h2 : a✝³ = a✝¹ ∧ isAlphaEqvVarList binders a✝² a✝
⊢ Holds D I V [] (def_ a✝³ a✝²) ↔ Holds D I V' [] (def_ a✝¹ a✝) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | induction F generalizing F' binders V V' | case cons
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
V V' : VarAssignment D
F... | case cons.pred_const_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
a✝¹ : PredNa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | all_goals
cases F' | case cons.pred_const_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
a✝¹ : PredNa... | case cons.pred_const_.pred_const_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | any_goals
simp only [isAlphaEqvAux] at h2 | case cons.pred_const_.pred_const_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
... | case cons.pred_const_.pred_const_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | case
pred_const_.pred_const_ X xs Y ys
| pred_var_.pred_var_ X xs Y ys =>
cases h2
case intro h2_left h2_right =>
simp only [Holds]
subst h2_left
congr! 1
exact aux_2 D binders xs ys V V' h1 h2_right | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | case true_.true_ | false_.false_ =>
simp only [Holds] | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
V V' : VarAssignment D
binders : L... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | case not_.not_ phi phi_ih phi' =>
simp only [Holds]
congr! 1
exact phi_ih V V' phi' binders h1 h2 | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
phi : Formula
phi_ih :
∀ (V V' :... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | cases F' | case cons.def_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
a✝¹ : DefName
a✝ : ... | case cons.def_.pred_const_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
a✝³ : D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | simp only [isAlphaEqvAux] at h2 | case cons.def_.def_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
a✝³ : DefName
... | case cons.def_.def_
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
a✝³ : DefName
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | cases h2 | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... | case intro
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | case intro h2_left h2_right =>
simp only [Holds]
subst h2_left
congr! 1
exact aux_2 D binders xs ys V V' h1 h2_right | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | simp only [Holds] | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | subst h2_left | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | congr! 1 | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : List VarName
V V... | case a.h.e'_4
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : Li... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | exact aux_2 D binders xs ys V V' h1 h2_right | case a.h.e'_4
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
X : PredName
xs : Li... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Alpha.lean | FOL.NV.isAlphaEqv_Holds_aux | [624, 1] | [734, 58] | cases h2 | D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
x x' : VarName
V V' : VarAssignmen... | case intro
D : Type
I : Interpretation D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
∀ (V V' : VarAssignment D) (F F' : Formula) (binders : List (VarName × VarName)),
AlphaEqvVarAssignment D binders V V' → isAlphaEqvAux binders F F' → (Holds D I V tail✝ F ↔ Holds D I V' tail✝ F')
x x' : VarName
V V' : V... |
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