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/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | obtain ⟨x, hx, ex⟩ : ∃ x, w ≺ x ∧ (Sum.inr $ Sum.inl x) = X := by
replace hWX : (IntDPCounterexampleModel M₁ M₂ w₁ w₂).Frame.Rel _ X := hWX;
simp [IntDPCounterexampleFrame] at hWX;
split at hWX;
all_goals simp_all; | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁... | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | subst ex | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, ... | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | exact ihq.mp $ h hx $ ihp.mpr hp | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | replace hWX : (IntDPCounterexampleModel M₁ M₂ w₁ w₂).Frame.Rel _ X := hWX | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisf... | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisf... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | simp [IntDPCounterexampleFrame] at hWX | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisf... | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisf... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | split at hWX | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisf... | case h_1
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | all_goals simp_all; | case h_1
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | simp_all | case h_6
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | simp only [Satisfies.imp_def] | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M... | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | intro h v hv hp | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M... | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | exact ihq.mpr $ h (by simpa [IntDPCounterexampleModel]) $ ihp.mp hp | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | simpa [IntDPCounterexampleModel] | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisf... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_left_on_IntDPCounterexampleModel | [70, 1] | [88, 79] | simp_all [IntDPCounterexampleModel, Satisfies.iff_models, Satisfies] | case hor
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p✝ q✝ : Formula α
a✝¹ : ∀ {w : M₁.World}, Satisfies M₁ w p✝ ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p✝
a✝ : ∀ {w : M₁.World}, Satisfies M₁ w ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | induction p using rec' generalizing w with
| himp p q ihp ihq =>
constructor;
. simp only [Satisfies.imp_def];
intro h X hWX hp;
obtain ⟨x, hx, ex⟩ : ∃ x, w ≺ x ∧ (Sum.inr $ Sum.inr x) = X := by
replace hWX : (IntDPCounterexampleModel M₁ M₂ w₁ w₂).Frame.Rel _ X := hWX;
simp [IntDPCounterexampleF... | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
w : M₂.World
w₁ : M₁.World
w₂ : M₂.World
⊢ Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | constructor | case himp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w ... | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | . simp only [Satisfies.imp_def];
intro h X hWX hp;
obtain ⟨x, hx, ex⟩ : ∃ x, w ≺ x ∧ (Sum.inr $ Sum.inr x) = X := by
replace hWX : (IntDPCounterexampleModel M₁ M₂ w₁ w₂).Frame.Rel _ X := hWX;
simp [IntDPCounterexampleFrame] at hWX;
split at hWX;
all_goals simp_all;
subst ex;
exact ihq.mp $ h hx ... | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | . simp only [Satisfies.imp_def];
intro h v hv hp;
exact ihq.mpr $ h (by simpa [IntDPCounterexampleModel]) $ ihp.mp hp; | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | simp only [Satisfies.imp_def] | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | intro h X hWX hp | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | obtain ⟨x, hx, ex⟩ : ∃ x, w ≺ x ∧ (Sum.inr $ Sum.inr x) = X := by
replace hWX : (IntDPCounterexampleModel M₁ M₂ w₁ w₂).Frame.Rel _ X := hWX;
simp [IntDPCounterexampleFrame] at hWX;
split at hWX;
all_goals simp_all; | case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂... | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | subst ex | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, ... | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | exact ihq.mp $ h hx $ ihp.mpr hp | case himp.mp.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | replace hWX : (IntDPCounterexampleModel M₁ M₂ w₁ w₂).Frame.Rel _ X := hWX | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q ↔ Satisf... | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q ↔ Satisf... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | simp [IntDPCounterexampleFrame] at hWX | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q ↔ Satisf... | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q ↔ Satisf... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | split at hWX | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q ↔ Satisf... | case h_1
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | all_goals simp_all; | case h_1
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | simp_all | case h_6
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | simp only [Satisfies.imp_def] | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | intro h v hv hp | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | exact ihq.mpr $ h (by simpa [IntDPCounterexampleModel]) $ ihp.mp hp | case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | simpa [IntDPCounterexampleModel] | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₂.World}, Satisfies M₂ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p
ihq : ∀ {w : M₂.World}, Satisfies M₂ w q ↔ Satisf... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.satisfies_right_on_IntDPCounterexampleModel | [90, 1] | [108, 79] | simp_all [IntDPCounterexampleModel, Satisfies.iff_models, Satisfies] | case hor
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p✝ q✝ : Formula α
a✝¹ : ∀ {w : M₂.World}, Satisfies M₂ w p✝ ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inr w)) p✝
a✝ : ∀ {w : M₂.World}, Satisfies M₂ w ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | contrapose | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
⊢ 𝐈𝐧𝐭 ⊢! p ⋎ q → 𝐈𝐧𝐭 ⊢! p ∨ 𝐈𝐧𝐭 ⊢! q | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
⊢ ¬(𝐈𝐧𝐭 ⊢! p ∨ 𝐈𝐧𝐭 ⊢! q) → ¬𝐈𝐧𝐭 ⊢! p ⋎ q |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | intro hC | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
⊢ ¬(𝐈𝐧𝐭 ⊢! p ∨ 𝐈𝐧𝐭 ⊢! q) → ¬𝐈𝐧𝐭 ⊢! p ⋎ q | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬(𝐈𝐧𝐭 ⊢! p ∨ 𝐈𝐧𝐭 ⊢! q)
⊢ ¬𝐈𝐧𝐭 ⊢! p ⋎ q |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | push_neg at hC | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬(𝐈𝐧𝐭 ⊢! p ∨ 𝐈𝐧𝐭 ⊢! q)
⊢ ¬𝐈𝐧𝐭 ⊢! p ⋎ q | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
⊢ ¬𝐈𝐧𝐭 ⊢! p ⋎ q |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | have ⟨hnp, hnq⟩ := hC | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
⊢ ¬𝐈𝐧𝐭 ⊢! p ⋎ q | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
⊢ ¬𝐈𝐧𝐭 ⊢! p ⋎ q |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | obtain ⟨Fp, _, Vp, hVp, wp, hp⟩ := by simpa [ValidOnFrameClass, ValidOnFrame, ValidOnModel] using not_imp_not.mpr complete! hnp; | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
⊢ ¬𝐈𝐧𝐭 ⊢! p ⋎ q | case intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w₁ w₂ : Fp.World}, w₁ ≺ w₂ → ∀ {... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | obtain ⟨Fq, _, Vq, hVq, wq, hq⟩ := by simpa [ValidOnFrameClass, ValidOnFrame, ValidOnModel] using not_imp_not.mpr complete! hnq; | case intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w₁ w₂ : Fp.World}, w₁ ≺ w₂ → ∀ {... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | apply (not_imp_not.mpr sound!) | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | simp [ValidOnFrameClass, ValidOnFrame, ValidOnModel] | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | let M : Model α := IntDPCounterexampleModel ⟨Fp, Vp, hVp⟩ ⟨Fq, Vq, hVq⟩ wp wq | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | existsi M.Frame | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | constructor | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp :... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | . apply iff_definability_memAxiomSetFrameClass AxiomSet.EFQ.definability |>.mpr;
trivial; | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp :... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | . existsi M.Valuation, M.hereditary, Sum.inl ();
constructor;
. exact not_imp_not.mpr (Satisfies.formula_hereditary (by apply Fp.Rel_refl)) $ satisfies_left_on_IntDPCounterexampleModel.not.mp hp;
. exact not_imp_not.mpr (Satisfies.formula_hereditary (by apply Fq.Rel_refl)) $ satisfies_right_on_IntDPCounterexample... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | simpa [ValidOnFrameClass, ValidOnFrame, ValidOnModel] using not_imp_not.mpr complete! hnp | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
⊢ ?m.380667 | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | simpa [ValidOnFrameClass, ValidOnFrame, ValidOnModel] using not_imp_not.mpr complete! hnq | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w₁ w₂ : Fp.World}, w₁ ≺ w₂ → ∀ {a : α}, Vp w₁ a → Vp w₂ a
wp : { Fr... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | apply iff_definability_memAxiomSetFrameClass AxiomSet.EFQ.definability |>.mpr | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp :... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp :... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | trivial | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp :... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | existsi M.Valuation, M.hereditary, Sum.inl () | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp ... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | constructor | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp ... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | . exact not_imp_not.mpr (Satisfies.formula_hereditary (by apply Fp.Rel_refl)) $ satisfies_left_on_IntDPCounterexampleModel.not.mp hp; | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α... | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | . exact not_imp_not.mpr (Satisfies.formula_hereditary (by apply Fq.Rel_refl)) $ satisfies_right_on_IntDPCounterexampleModel.not.mp hq; | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | exact not_imp_not.mpr (Satisfies.formula_hereditary (by apply Fp.Rel_refl)) $ satisfies_left_on_IntDPCounterexampleModel.not.mp hp | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right.left
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | apply Fp.Rel_refl | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w₁ w₂ : Fp.World}, w₁ ≺ w₂ → ∀ {a : α}, Vp w₁ a → Vp w₂ a
wp : { F... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | exact not_imp_not.mpr (Satisfies.formula_hereditary (by apply Fq.Rel_refl)) $ satisfies_right_on_IntDPCounterexampleModel.not.mp hq | case intro.intro.intro.intro.intro.intro.intro.intro.intro.intro.right.right
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Propositional/Superintuitionistic/Kripke/DP.lean | LO.Propositional.Superintuitionistic.Kripke.disjunctive_int | [110, 1] | [127, 139] | apply Fq.Rel_refl | α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p q : Formula α
M₁ M₂ : Model α
hC : ¬𝐈𝐧𝐭 ⊢! p ∧ ¬𝐈𝐧𝐭 ⊢! q
hnp : ¬𝐈𝐧𝐭 ⊢! p
hnq : ¬𝐈𝐧𝐭 ⊢! q
Fp : Frame' α
left✝¹ : Fp ∈ 𝔽(𝗘𝗙𝗤)
Vp : Valuation Fp.World α
hVp : ∀ {w₁ w₂ : Fp.World}, w₁ ≺ w₂ → ∀ {a : α}, Vp w₁ a → Vp w₂ a
wp : { F... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.mem_set_iff | [49, 1] | [49, 89] | simp [set] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
x : β
a : α
⊢ x ∈ set a ↔ x ∈ a | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.subset_iff_set_subset_set | [51, 1] | [51, 95] | simp [subset_iff, set] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
a b : α
⊢ a ⊆ b ↔ set a ⊆ set b | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.empty_subset | [61, 1] | [61, 67] | simp [subset_iff] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
a : α
⊢ ∅ ⊆ a | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.mem_cons | [63, 1] | [63, 80] | simp [mem_cons_iff] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
a : α
x : β
⊢ x ∈ cons x a | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.subset_cons | [65, 1] | [65, 102] | simp [subset_iff, mem_cons_iff] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
a : α
x : β
⊢ a ⊆ cons x a | β : Type u_1
α : Type u_2
inst✝ : Collection β α
a : α
x : β
⊢ ∀ x_1 ∈ a, x_1 = x ∨ x_1 ∈ a |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.subset_cons | [65, 1] | [65, 102] | tauto | β : Type u_1
α : Type u_2
inst✝ : Collection β α
a : α
x : β
⊢ ∀ x_1 ∈ a, x_1 = x ∨ x_1 ∈ a | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.set_empty | [67, 1] | [67, 64] | ext | β : Type u_1
α : Type u_2
inst✝ : Collection β α
⊢ set ∅ = ∅ | case h
β : Type u_1
α : Type u_2
inst✝ : Collection β α
x✝ : β
⊢ x✝ ∈ set ∅ ↔ x✝ ∈ ∅ |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.set_empty | [67, 1] | [67, 64] | simp [set] | case h
β : Type u_1
α : Type u_2
inst✝ : Collection β α
x✝ : β
⊢ x✝ ∈ set ∅ ↔ x✝ ∈ ∅ | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.set_cons | [69, 1] | [69, 97] | ext | β : Type u_1
α : Type u_2
inst✝ : Collection β α
z : β
a : α
⊢ set (cons z a) = insert z (set a) | case h
β : Type u_1
α : Type u_2
inst✝ : Collection β α
z : β
a : α
x✝ : β
⊢ x✝ ∈ set (cons z a) ↔ x✝ ∈ insert z (set a) |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.set_cons | [69, 1] | [69, 97] | simp [set] | case h
β : Type u_1
α : Type u_2
inst✝ : Collection β α
z : β
a : α
x✝ : β
⊢ x✝ ∈ set (cons z a) ↔ x✝ ∈ insert z (set a) | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.empty_finite | [73, 1] | [73, 64] | simp [Finite] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
⊢ Finite ∅ | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.cons_finite_iff | [78, 1] | [79, 79] | simp | β : Type u_1
α : Type u_2
inst✝ : Collection β α
z : β
a : α
h : Finite (cons z a)
⊢ a ⊆ cons z a | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.cons_finite_iff | [78, 1] | [79, 79] | simpa [Finite] using Set.Finite.insert z | β : Type u_1
α : Type u_2
inst✝ : Collection β α
z : β
a : α
⊢ Finite a → Finite (cons z a) | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.mem_list_toCollection | [91, 1] | [92, 46] | induction l <;> simp [List.toCollection, *] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
x : β
l : List β
⊢ x ∈ l.toCollection ↔ x ∈ l | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.mem_finset_toCollection | [94, 1] | [94, 129] | simp [Finset.toCollection] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
x : β
s : Finset β
⊢ x ∈ s.toCollection ↔ x ∈ s | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.list_toCollection_finite | [96, 1] | [96, 107] | simp [Finite, set] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
l : List β
⊢ Finite l.toCollection | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Collection.finset_toCollection_finite | [98, 1] | [98, 111] | simp [Finite, set] | β : Type u_1
α : Type u_2
inst✝ : Collection β α
s : Finset β
⊢ Finite s.toCollection | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/Vorspiel/Collection.lean | Set.collection_finite_iff | [110, 1] | [110, 112] | simp [Collection.Finite] | α : Type u_1
s : Set α
⊢ Collection.Finite s ↔ s.Finite | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Structure.val_lMap_add₁ | [115, 1] | [117, 65] | induction t <;> simp [Semiterm.val, Language.Hom.func_add₁, *] | L₁ : Language
L₂ : Language
M : Type u_1
str₁ : Structure L₁ M
str₂ : Structure L₂ M
μ : Type u_2
n : ℕ
t : Semiterm L₁ μ n
e : Fin n → M
ε : μ → M
⊢ Semiterm.val (add L₁ L₂ M) e ε (Semiterm.lMap (Language.Hom.add₁ L₁ L₂) t) = Semiterm.val str₁ e ε t | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Structure.val_lMap_add₂ | [119, 1] | [121, 65] | induction t <;> simp [Semiterm.val, Language.Hom.func_add₂, *] | L₁ : Language
L₂ : Language
M : Type u_1
str₁ : Structure L₁ M
str₂ : Structure L₂ M
μ : Type u_2
n : ℕ
t : Semiterm L₂ μ n
e : Fin n → M
ε : μ → M
⊢ Semiterm.val (add L₁ L₂ M) e ε (Semiterm.lMap (Language.Hom.add₂ L₁ L₂) t) = Semiterm.val str₂ e ε t | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Structure.eval_lMap_add₁ | [123, 1] | [128, 74] | induction p using Semiformula.rec' <;>
simp [*, Language.Hom.rel_add₁, Semiformula.eval_rel,
Semiformula.lMap_rel, Semiformula.eval_nrel, Semiformula.lMap_nrel] | L₁ : Language
L₂ : Language
M : Type u_1
str₁ : Structure L₁ M
str₂ : Structure L₂ M
μ : Type u_2
n : ℕ
p : Semiformula L₁ μ n
e : Fin n → M
ε : μ → M
⊢ (Semiformula.Eval (add L₁ L₂ M) e ε) ((Semiformula.lMap (Language.Hom.add₁ L₁ L₂)) p) ↔ (Semiformula.Eval str₁ e ε) p | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Structure.eval_lMap_add₂ | [130, 1] | [135, 74] | induction p using Semiformula.rec' <;>
simp [*, Language.Hom.rel_add₂, Semiformula.eval_rel,
Semiformula.lMap_rel, Semiformula.eval_nrel, Semiformula.lMap_nrel] | L₁ : Language
L₂ : Language
M : Type u_1
str₁ : Structure L₁ M
str₂ : Structure L₂ M
μ : Type u_2
n : ℕ
p : Semiformula L₂ μ n
e : Fin n → M
ε : μ → M
⊢ (Semiformula.Eval (add L₁ L₂ M) e ε) ((Semiformula.lMap (Language.Hom.add₂ L₁ L₂)) p) ↔ (Semiformula.Eval str₂ e ε) p | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Structure.val_lMap_sigma | [151, 1] | [153, 66] | induction t <;> simp [Semiterm.val, Language.Hom.func_sigma, *] | ι : Type u_4
L : ι → Language
M : Type u_1
str : (i : ι) → Structure (L i) M
i : ι
μ : Type u_2
n : ℕ
t : Semiterm (L i) μ n
e : Fin n → M
ε : μ → M
⊢ Semiterm.val (sigma L M) e ε (Semiterm.lMap (Language.Hom.sigma L i) t) = Semiterm.val (str i) e ε t | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Structure.eval_lMap_sigma | [155, 1] | [160, 74] | induction p using Semiformula.rec' <;>
simp [*, Language.Hom.rel_sigma, Semiformula.eval_rel,
Semiformula.lMap_rel, Semiformula.eval_nrel, Semiformula.lMap_nrel] | ι : Type u_4
L : ι → Language
M : Type u_1
str : (i : ι) → Structure (L i) M
i : ι
μ : Type u_2
n : ℕ
p : Semiformula (L i) μ n
e : Fin n → M
ε : μ → M
⊢ (Semiformula.Eval (sigma L M) e ε) ((Semiformula.lMap (Language.Hom.sigma L i)) p) ↔ (Semiformula.Eval (str i) e ε) p | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Semiterm.valm_uLift | [180, 1] | [182, 46] | induction t <;> simp [*, Semiterm.val_func] | L : Language
M : Type v
inst✝ : Structure L M
n : ℕ
ξ : Type u_1
e : Fin n → ULift.{v', v} M
ε : ξ → ULift.{v', v} M
t : Semiterm L ξ n
⊢ valm (ULift.{v', v} M) e ε t = { down := valm M (fun i => (e i).down) (fun i => (ε i).down) t } | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.Semiformula.evalm_uLift | [184, 1] | [187, 101] | induction p using Semiformula.rec' <;>
simp [*, Semiformula.eval_rel, Semiformula.eval_nrel, Semiterm.valm_uLift, Matrix.comp_vecCons'] | L : Language
M : Type v
inst✝ : Structure L M
n : ℕ
ξ : Type u_1
e : Fin n → ULift.{v', v} M
ε : ξ → ULift.{v', v} M
p : Semiformula L ξ n
⊢ (Evalm (ULift.{v', v} M) e ε) p ↔ (Evalm M (fun i => (e i).down) fun i => (ε i).down) p | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.uLift_elementaryEquiv | [191, 1] | [192, 86] | intro σ | L : Language
M : Type v
inst✝¹ : Structure L M
inst✝ : Nonempty M
⊢ ULift.{v', v} M ≡ₑ[L] M | L : Language
M : Type v
inst✝¹ : Structure L M
inst✝ : Nonempty M
σ : Sentence L
⊢ ULift.{v', v} M ⊧ₘ σ ↔ M ⊧ₘ σ |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Model.lean | LO.FirstOrder.uLift_elementaryEquiv | [191, 1] | [192, 86] | simp [models_iff, Semiformula.evalm_uLift, Matrix.empty_eq, Empty.eq_elim] | L : Language
M : Type v
inst✝¹ : Structure L M
inst✝ : Nonempty M
σ : Sentence L
⊢ ULift.{v', v} M ⊧ₘ σ ↔ M ⊧ₘ σ | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Semiterm.substs_varSumInL | [16, 1] | [17, 111] | simp [varSumInL, Matrix.vecAppend_eq_ite] | L : Language
μ : Type u_1
inst✝ : Semiformula.Operator.Eq L
k n : ℕ
w₁ w₂ : Fin k → Semiterm L μ n
i : Fin k
⊢ (Rew.substs (Matrix.vecAppend ⋯ w₁ w₂)) (varSumInL i) = w₁ i | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Semiterm.substs_varSumInR | [19, 1] | [20, 111] | simp [varSumInR, Matrix.vecAppend_eq_ite] | L : Language
μ : Type u_1
inst✝ : Semiformula.Operator.Eq L
k n : ℕ
w₁ w₂ : Fin k → Semiterm L μ n
i : Fin k
⊢ (Rew.substs (Matrix.vecAppend ⋯ w₁ w₂)) (varSumInR i) = w₂ i | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Semiterm.emb_varSumInL | [22, 1] | [23, 95] | simp [varSumInL] | L : Language
μ : Type u_1
inst✝¹ : Semiformula.Operator.Eq L
k : ℕ
o : Type u_2
inst✝ : IsEmpty o
i : Fin k
⊢ Rew.emb (varSumInL i) = varSumInL i | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Semiterm.emb_varSumInR | [25, 1] | [26, 95] | simp [varSumInR] | L : Language
μ : Type u_1
inst✝¹ : Semiformula.Operator.Eq L
k : ℕ
o : Type u_2
inst✝ : IsEmpty o
i : Fin k
⊢ Rew.emb (varSumInR i) = varSumInR i | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | intro σ h | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
⊢ ∀ ⦃f : Sentence L⦄, f ∈ 𝐄𝐐 → inst✝¹.toStruc ⊧ f | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
σ : Sentence L
h : σ ∈ 𝐄𝐐
⊢ inst✝¹.toStruc ⊧ σ |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | cases h <;> simp [models_def, Semiformula.vecEq, Semiterm.val_func] | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
σ : Sentence L
h : σ ∈ 𝐄𝐐
⊢ inst✝¹.toStruc ⊧ σ | case funcExt
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
⊢ ∀ (e : Fin (k✝ + k✝) → M),
(∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) =
Semiterm.val inst✝¹... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | case relExt r =>
simp [Semiformula.eval_rel]; intro e h; simp [congr_arg (rel r) (funext h)] | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
r : L.Rel k✝
⊢ ∀ (e : Fin (k✝ + k✝) → M),
(∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) =
Semiterm.val inst✝¹ e Empty.elim (... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | intro e h | case funcExt
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
⊢ ∀ (e : Fin (k✝ + k✝) → M),
(∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) =
Semiterm.val inst✝¹... | case funcExt
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim (Semit... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | congr | case funcExt
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim (Semit... | case funcExt.e_a
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim (S... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | funext i | case funcExt.e_a
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim (S... | case funcExt.e_a.h
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim ... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | exact h i | case funcExt.e_a.h
L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
f✝ : L.Func k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim ... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | simp [Semiformula.eval_rel] | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
r : L.Rel k✝
⊢ ∀ (e : Fin (k✝ + k✝) → M),
(∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) =
Semiterm.val inst✝¹ e Empty.elim (... | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
r : L.Rel k✝
⊢ ∀ (e : Fin (k✝ + k✝) → M),
(∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) =
Semiterm.val inst✝¹ e Empty.elim (... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | intro e h | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
r : L.Rel k✝
⊢ ∀ (e : Fin (k✝ + k✝) → M),
(∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) =
Semiterm.val inst✝¹ e Empty.elim (... | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
r : L.Rel k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInR i... |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.models_eqAxiom | [83, 1] | [88, 81] | simp [congr_arg (rel r) (funext h)] | L : Language
μ : Type u_1
inst✝³ : Semiformula.Operator.Eq L
M : Type u
inst✝² : Nonempty M
inst✝¹ : Structure L M
inst✝ : Structure.Eq L M
k✝ : ℕ
r : L.Rel k✝
e : Fin (k✝ + k✝) → M
h :
∀ (i : Fin k✝),
Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInL i) = Semiterm.val inst✝¹ e Empty.elim (Semiterm.varSumInR i... | no goals |
https://github.com/iehality/lean4-logic.git | 9cee05ba7c48d586f7e488ef44f6445dea8102f8 | Logic/FirstOrder/Basic/Eq.lean | LO.FirstOrder.Structure.Eq.eqv_refl | [104, 1] | [107, 15] | have : M ⊧ₘ “∀ x, x = x” := H.realize (Theory.eqAxiom.refl (L := L)) | L : Language
μ : Type u_1
inst✝² : Operator.Eq L
M : Type u
inst✝¹ : Nonempty M
inst✝ : Structure L M
H : M ⊧ₘ* 𝐄𝐐
a : M
⊢ eqv L a a | L : Language
μ : Type u_1
inst✝² : Operator.Eq L
M : Type u
inst✝¹ : Nonempty M
inst✝ : Structure L M
H : M ⊧ₘ* 𝐄𝐐
a : M
this : M ⊧ₘ (“∀' #0 = #0”)
⊢ eqv L a a |
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