Split (1)

train · 219k rows

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M	input stringlengths 73 2.09M
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/DFT.lean	dft_iff	[884, 1]	[900, 50]	intro ⟨s, h1, h2⟩	case mpr α : Type inst✝ : DecidableEq α g : Graph α S : List α s' : α ⊢ (∃ s ∈ S, Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s s') → s' ∈ reachable_from_list g S	case mpr α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S h2 : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s s' ⊢ s' ∈ reachable_from_list g S	Please generate a tactic in lean4 to solve the state. STATE: case mpr α : Type inst✝ : DecidableEq α g : Graph α S : List α s' : α ⊢ (∃ s ∈ S, Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s s') → s' ∈ reachable_from_list g S TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/DFT.lean	dft_iff	[884, 1]	[900, 50]	induction h2 with \| refl => exact reachable_from_list.base _ h1 \| tail _ h ih => have ⟨_, h3, h4⟩ := h exact reachable_from_list.step _ _ h3 h4 ih	case mpr α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S h2 : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s s' ⊢ s' ∈ reachable_from_list g S	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mpr α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S h2 : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s s' ⊢ s' ∈ reachable_from_list g S TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/DFT.lean	dft_iff	[884, 1]	[900, 50]	exact reachable_from_list.base _ h1	case mpr.refl α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S ⊢ s ∈ reachable_from_list g S	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mpr.refl α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S ⊢ s ∈ reachable_from_list g S TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/DFT.lean	dft_iff	[884, 1]	[900, 50]	have ⟨_, h3, h4⟩ := h	case mpr.tail α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S b✝ c✝ : α a✝ : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s b✝ h : ∃ l, (b✝, l) ∈ g ∧ c✝ ∈ l ih : b✝ ∈ reachable_from_list g S ⊢ c✝ ∈ reachable_from_list g S	case mpr.tail α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S b✝ c✝ : α a✝ : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s b✝ h : ∃ l, (b✝, l) ∈ g ∧ c✝ ∈ l ih : b✝ ∈ reachable_from_list g S w✝ : List α h3 : (b✝, w✝) ∈ g h4 : c✝ ∈ w✝ ⊢ c✝ ∈ reachable_from_list g S	Please generate a tactic in lean4 to solve the state. STATE: case mpr.tail α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S b✝ c✝ : α a✝ : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s b✝ h : ∃ l, (b✝, l) ∈ g ∧ c✝ ∈ l ih : b✝ ∈ reachable_from_list g S ⊢ c✝ ∈ reachable_from_list g...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/DFT.lean	dft_iff	[884, 1]	[900, 50]	exact reachable_from_list.step _ _ h3 h4 ih	case mpr.tail α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S b✝ c✝ : α a✝ : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s b✝ h : ∃ l, (b✝, l) ∈ g ∧ c✝ ∈ l ih : b✝ ∈ reachable_from_list g S w✝ : List α h3 : (b✝, w✝) ∈ g h4 : c✝ ∈ w✝ ⊢ c✝ ∈ reachable_from_list g S	no goals	Please generate a tactic in lean4 to solve the state. STATE: case mpr.tail α : Type inst✝ : DecidableEq α g : Graph α S : List α s' s : α h1 : s ∈ S b✝ c✝ : α a✝ : Relation.ReflTransGen (fun a b => ∃ l, (a, l) ∈ g ∧ b ∈ l) s b✝ h : ∃ l, (b✝, l) ∈ g ∧ c✝ ∈ l ih : b✝ ∈ reachable_from_list g S w✝ : List α h3 : (b✝, w✝) ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	DA.memAccepts	[145, 1]	[151, 67]	rfl	α σ : Type D : DA α σ input : List α ⊢ D.accepts input ↔ D.evalFrom D.startingState input ∈ D.acceptingStates	no goals	Please generate a tactic in lean4 to solve the state. STATE: α σ : Type D : DA α σ input : List α ⊢ D.accepts input ↔ D.evalFrom D.startingState input ∈ D.acceptingStates TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NA.memAccepts	[154, 1]	[161, 38]	rfl	α σ : Type N : NA α σ input : List α ⊢ N.accepts input ↔ ∃ s ∈ N.evalFrom N.startingStates input, s ∈ N.acceptingStates	no goals	Please generate a tactic in lean4 to solve the state. STATE: α σ : Type N : NA α σ input : List α ⊢ N.accepts input ↔ ∃ s ∈ N.evalFrom N.startingStates input, s ∈ N.acceptingStates TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	ext cs	α σ : Type N : NA α σ ⊢ N.toDA.accepts = N.accepts	case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.accepts cs ↔ N.accepts cs	Please generate a tactic in lean4 to solve the state. STATE: α σ : Type N : NA α σ ⊢ N.toDA.accepts = N.accepts TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	simp only [DA.memAccepts]	case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.accepts cs ↔ N.accepts cs	case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.evalFrom N.toDA.startingState cs ∈ N.toDA.acceptingStates ↔ N.accepts cs	Please generate a tactic in lean4 to solve the state. STATE: case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.accepts cs ↔ N.accepts cs TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	simp only [NA.memAccepts]	case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.evalFrom N.toDA.startingState cs ∈ N.toDA.acceptingStates ↔ N.accepts cs	case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.evalFrom N.toDA.startingState cs ∈ N.toDA.acceptingStates ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates	Please generate a tactic in lean4 to solve the state. STATE: case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.evalFrom N.toDA.startingState cs ∈ N.toDA.acceptingStates ↔ N.accepts cs TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	simp only [NA.toDA]	case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.evalFrom N.toDA.startingState cs ∈ N.toDA.acceptingStates ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates	case h.a α σ : Type N : NA α σ cs : List α ⊢ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs ∈ {S \| ∃ s ∈ S, s ∈ N.acceptingStates} ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates	Please generate a tactic in lean4 to solve the state. STATE: case h.a α σ : Type N : NA α σ cs : List α ⊢ N.toDA.evalFrom N.toDA.startingState cs ∈ N.toDA.acceptingStates ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	simp	case h.a α σ : Type N : NA α σ cs : List α ⊢ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs ∈ {S \| ∃ s ∈ S, s ∈ N.acceptingStates} ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates	case h.a α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptingStates) ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.accepti...	Please generate a tactic in lean4 to solve the state. STATE: case h.a α σ : Type N : NA α σ cs : List α ⊢ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs ∈ {S \| ∃ s ∈ S, s ∈ N.acceptingStates} ↔ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	constructor	case h.a α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptingStates) ↔ ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.accepti...	case h.a.mp α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptingStates) → ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acce...	Please generate a tactic in lean4 to solve the state. STATE: case h.a α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptingStat...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	all_goals simp intro s a1 a2 apply Exists.intro s tauto	case h.a.mp α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptingStates) → ∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acce...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h.a.mp α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptingS...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	simp	case h.a.mpr α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates) → ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acc...	case h.a.mpr α σ : Type N : NA α σ cs : List α ⊢ ∀ x ∈ N.evalFrom N.startingStates cs, x ∈ N.acceptingStates → ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, ...	Please generate a tactic in lean4 to solve the state. STATE: case h.a.mpr α σ : Type N : NA α σ cs : List α ⊢ (∃ s ∈ N.evalFrom N.startingStates cs, s ∈ N.acceptingStates) → ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStat...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	intro s a1 a2	case h.a.mpr α σ : Type N : NA α σ cs : List α ⊢ ∀ x ∈ N.evalFrom N.startingStates cs, x ∈ N.acceptingStates → ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, ...	case h.a.mpr α σ : Type N : NA α σ cs : List α s : σ a1 : s ∈ N.evalFrom N.startingStates cs a2 : s ∈ N.acceptingStates ⊢ ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptin...	Please generate a tactic in lean4 to solve the state. STATE: case h.a.mpr α σ : Type N : NA α σ cs : List α ⊢ ∀ x ∈ N.evalFrom N.startingStates cs, x ∈ N.acceptingStates → ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acc...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	apply Exists.intro s	case h.a.mpr α σ : Type N : NA α σ cs : List α s : σ a1 : s ∈ N.evalFrom N.startingStates cs a2 : s ∈ N.acceptingStates ⊢ ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs, s ∈ N.acceptin...	case h.a.mpr α σ : Type N : NA α σ cs : List α s : σ a1 : s ∈ N.evalFrom N.startingStates cs a2 : s ∈ N.acceptingStates ⊢ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs ∧ s ∈ N.acceptingStat...	Please generate a tactic in lean4 to solve the state. STATE: case h.a.mpr α σ : Type N : NA α σ cs : List α s : σ a1 : s ∈ N.evalFrom N.startingStates cs a2 : s ∈ N.acceptingStates ⊢ ∃ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingState...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/Compute.lean	NAtoDAisEquiv	[167, 1]	[183, 10]	tauto	case h.a.mpr α σ : Type N : NA α σ cs : List α s : σ a1 : s ∈ N.evalFrom N.startingStates cs a2 : s ∈ N.acceptingStates ⊢ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.evalFrom N.startingStates cs ∧ s ∈ N.acceptingStat...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h.a.mpr α σ : Type N : NA α σ cs : List α s : σ a1 : s ∈ N.evalFrom N.startingStates cs a2 : s ∈ N.acceptingStates ⊢ s ∈ { step := N.stepSet, startingState := N.startingStates, acceptingStates := {S \| ∃ s ∈ S, s ∈ N.acceptingStates} }.e...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_prime	[136, 1]	[146, 8]	induction F	F : Formula V : VarBoolAssignment h1 : F.IsPrime ⊢ evalPrime V F = (V F = true)	case pred_const_ V : VarBoolAssignment a✝¹ : PredName a✝ : List VarName h1 : (pred_const_ a✝¹ a✝).IsPrime ⊢ evalPrime V (pred_const_ a✝¹ a✝) = (V (pred_const_ a✝¹ a✝) = true) case pred_var_ V : VarBoolAssignment a✝¹ : PredName a✝ : List VarName h1 : (pred_var_ a✝¹ a✝).IsPrime ⊢ evalPrime V (pred_var_ a✝¹ a✝) = (V (pre...	Please generate a tactic in lean4 to solve the state. STATE: F : Formula V : VarBoolAssignment h1 : F.IsPrime ⊢ evalPrime V F = (V F = true) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_prime	[136, 1]	[146, 8]	case true_ \| false_ \| not_ \| imp_ \| and_ \| or_ \| iff_ => simp only [Formula.IsPrime] at h1	V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrime V a✝¹ = (V a✝¹ = true) a_ih✝ : a✝.IsPrime → evalPrime V a✝ = (V a✝ = true) h1 : (a✝¹.iff_ a✝).IsPrime ⊢ evalPrime V (a✝¹.iff_ a✝) = (V (a✝¹.iff_ a✝) = true)	no goals	Please generate a tactic in lean4 to solve the state. STATE: V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrime V a✝¹ = (V a✝¹ = true) a_ih✝ : a✝.IsPrime → evalPrime V a✝ = (V a✝ = true) h1 : (a✝¹.iff_ a✝).IsPrime ⊢ evalPrime V (a✝¹.iff_ a✝) = (V (a✝¹.iff_ a✝) = true) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_prime	[136, 1]	[146, 8]	case pred_const_ \| pred_var_ \| eq_ \| forall_ \| exists_ \| def_ => rfl	V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName h1 : (def_ a✝¹ a✝).IsPrime ⊢ evalPrime V (def_ a✝¹ a✝) = (V (def_ a✝¹ a✝) = true)	no goals	Please generate a tactic in lean4 to solve the state. STATE: V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName h1 : (def_ a✝¹ a✝).IsPrime ⊢ evalPrime V (def_ a✝¹ a✝) = (V (def_ a✝¹ a✝) = true) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_prime	[136, 1]	[146, 8]	simp only [Formula.IsPrime] at h1	V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrime V a✝¹ = (V a✝¹ = true) a_ih✝ : a✝.IsPrime → evalPrime V a✝ = (V a✝ = true) h1 : (a✝¹.iff_ a✝).IsPrime ⊢ evalPrime V (a✝¹.iff_ a✝) = (V (a✝¹.iff_ a✝) = true)	no goals	Please generate a tactic in lean4 to solve the state. STATE: V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrime V a✝¹ = (V a✝¹ = true) a_ih✝ : a✝.IsPrime → evalPrime V a✝ = (V a✝ = true) h1 : (a✝¹.iff_ a✝).IsPrime ⊢ evalPrime V (a✝¹.iff_ a✝) = (V (a✝¹.iff_ a✝) = true) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_prime	[136, 1]	[146, 8]	rfl	V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName h1 : (def_ a✝¹ a✝).IsPrime ⊢ evalPrime V (def_ a✝¹ a✝) = (V (def_ a✝¹ a✝) = true)	no goals	Please generate a tactic in lean4 to solve the state. STATE: V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName h1 : (def_ a✝¹ a✝).IsPrime ⊢ evalPrime V (def_ a✝¹ a✝) = (V (def_ a✝¹ a✝) = true) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	induction F	F : Formula σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ F) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) F	case pred_const_ σ : Formula → Formula V : VarBoolAssignment a✝¹ : PredName a✝ : List VarName ⊢ evalPrime V (substPrime σ (pred_const_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (pred_const_ a✝¹ a✝) case pred_var_ σ : Formula → Formula V : VarBoolAssignment a✝¹ : PredName a✝ : List VarName ⊢ evalPrime ...	Please generate a tactic in lean4 to solve the state. STATE: F : Formula σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ F) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) F TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	case pred_const_ \| pred_var_ \| eq_ \| forall_ \| exists_ \| def_ => simp only [Formula.substPrime] simp only [Formula.evalPrime] simp	σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (substPrime σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝)	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (substPrime σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	case true_ \| false_ => rfl	σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ false_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) false_	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ false_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) false_ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	case not_ phi phi_ih => simp only [Formula.substPrime] simp only [Formula.evalPrime] congr! 1	σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi.not_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi.not_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	case imp_ phi psi phi_ih psi_ih \| and_ phi psi phi_ih psi_ih \| or_ phi psi phi_ih psi_ih \| iff_ phi psi phi_ih psi_ih => simp only [Formula.substPrime] simp only [Formula.evalPrime] congr! 1	σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPrime V (substPrime σ (phi.iff_ psi)) ↔ evalPrime (fun H => deci...	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPri...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp only [Formula.substPrime]	σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (substPrime σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝)	σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝)	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (substPrime σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp only [Formula.evalPrime]	σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝)	σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (σ (def_ a✝¹ a✝)) ↔ decide (evalPrime V (σ (def_ a✝¹ a✝))) = true	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (σ (def_ a✝¹ a✝)) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) (def_ a✝¹ a✝) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp	σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (σ (def_ a✝¹ a✝)) ↔ decide (evalPrime V (σ (def_ a✝¹ a✝))) = true	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName ⊢ evalPrime V (σ (def_ a✝¹ a✝)) ↔ decide (evalPrime V (σ (def_ a✝¹ a✝))) = true TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	rfl	σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ false_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) false_	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ false_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) false_ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp only [Formula.substPrime]	σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi.not_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_	σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi).not_ ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi.not_) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp only [Formula.evalPrime]	σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi).not_ ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_	σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ ¬evalPrime V (substPrime σ phi) ↔ ¬evalPrime (fun H => decide (evalPrime V (σ H))) phi	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ evalPrime V (substPrime σ phi).not_ ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi.not_ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	congr! 1	σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ ¬evalPrime V (substPrime σ phi) ↔ ¬evalPrime (fun H => decide (evalPrime V (σ H))) phi	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi ⊢ ¬evalPrime V (substPrime σ phi) ↔ ¬evalPrime (fun H => decide (evalPrime V (σ H))) phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp only [Formula.substPrime]	σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPrime V (substPrime σ (phi.iff_ psi)) ↔ evalPrime (fun H => deci...	σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPrime V ((substPrime σ phi).iff_ (substPrime σ psi)) ↔ evalP...	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPri...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	simp only [Formula.evalPrime]	σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPrime V ((substPrime σ phi).iff_ (substPrime σ psi)) ↔ evalP...	σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ (evalPrime V (substPrime σ phi) ↔ evalPrime V (substPrime σ psi)) ↔ ...	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ evalPri...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrime_substPrime_eq_evalPrime_evalPrime	[193, 1]	[218, 13]	congr! 1	σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ (evalPrime V (substPrime σ phi) ↔ evalPrime V (substPrime σ psi)) ↔ ...	no goals	Please generate a tactic in lean4 to solve the state. STATE: σ : Formula → Formula V : VarBoolAssignment phi psi : Formula phi_ih : evalPrime V (substPrime σ phi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) phi psi_ih : evalPrime V (substPrime σ psi) ↔ evalPrime (fun H => decide (evalPrime V (σ H))) psi ⊢ (evalPr...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.isTautoPrime_imp_isTautoPrime_substPrime	[221, 1]	[232, 11]	simp only [Formula.IsTautoPrime] at h1	P : Formula h1 : P.IsTautoPrime σ : Formula → Formula ⊢ (substPrime σ P).IsTautoPrime	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula ⊢ (substPrime σ P).IsTautoPrime	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : P.IsTautoPrime σ : Formula → Formula ⊢ (substPrime σ P).IsTautoPrime TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.isTautoPrime_imp_isTautoPrime_substPrime	[221, 1]	[232, 11]	simp only [Formula.IsTautoPrime]	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula ⊢ (substPrime σ P).IsTautoPrime	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula ⊢ ∀ (V : VarBoolAssignment), evalPrime V (substPrime σ P)	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula ⊢ (substPrime σ P).IsTautoPrime TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.isTautoPrime_imp_isTautoPrime_substPrime	[221, 1]	[232, 11]	intro V	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula ⊢ ∀ (V : VarBoolAssignment), evalPrime V (substPrime σ P)	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ P)	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula ⊢ ∀ (V : VarBoolAssignment), evalPrime V (substPrime σ P) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.isTautoPrime_imp_isTautoPrime_substPrime	[221, 1]	[232, 11]	simp only [evalPrime_substPrime_eq_evalPrime_evalPrime P σ V]	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ P)	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime (fun H => decide (evalPrime V (σ H))) P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime V (substPrime σ P) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.isTautoPrime_imp_isTautoPrime_substPrime	[221, 1]	[232, 11]	apply h1	P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime (fun H => decide (evalPrime V (σ H))) P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : ∀ (V : VarBoolAssignment), evalPrime V P σ : Formula → Formula V : VarBoolAssignment ⊢ evalPrime (fun H => decide (evalPrime V (σ H))) P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	simp only [IsProof]	P : Formula ⊢ IsProof (P.imp_ P)	P : Formula ⊢ IsDeduct ∅ (P.imp_ P)	Please generate a tactic in lean4 to solve the state. STATE: P : Formula ⊢ IsProof (P.imp_ P) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	apply IsDeduct.mp_ (P.imp_ (P.imp_ P))	P : Formula ⊢ IsDeduct ∅ (P.imp_ P)	case a P : Formula ⊢ IsDeduct ∅ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P)) case a P : Formula ⊢ IsDeduct ∅ (P.imp_ (P.imp_ P))	Please generate a tactic in lean4 to solve the state. STATE: P : Formula ⊢ IsDeduct ∅ (P.imp_ P) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	apply IsDeduct.mp_ (P.imp_ ((P.imp_ P).imp_ P))	case a P : Formula ⊢ IsDeduct ∅ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P))	case a.a P : Formula ⊢ IsDeduct ∅ ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P))) case a.a P : Formula ⊢ IsDeduct ∅ (P.imp_ ((P.imp_ P).imp_ P))	Please generate a tactic in lean4 to solve the state. STATE: case a P : Formula ⊢ IsDeduct ∅ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	apply IsDeduct.axiom_	case a.a P : Formula ⊢ IsDeduct ∅ ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P)))	case a.a.a P : Formula ⊢ IsAxiom ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P)))	Please generate a tactic in lean4 to solve the state. STATE: case a.a P : Formula ⊢ IsDeduct ∅ ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	exact IsAxiom.prop_2_ P (P.imp_ P) P	case a.a.a P : Formula ⊢ IsAxiom ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P)))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a P : Formula ⊢ IsAxiom ((P.imp_ ((P.imp_ P).imp_ P)).imp_ ((P.imp_ (P.imp_ P)).imp_ (P.imp_ P))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	apply IsDeduct.axiom_	case a.a P : Formula ⊢ IsDeduct ∅ (P.imp_ ((P.imp_ P).imp_ P))	case a.a.a P : Formula ⊢ IsAxiom (P.imp_ ((P.imp_ P).imp_ P))	Please generate a tactic in lean4 to solve the state. STATE: case a.a P : Formula ⊢ IsDeduct ∅ (P.imp_ ((P.imp_ P).imp_ P)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	exact IsAxiom.prop_1_ P (P.imp_ P)	case a.a.a P : Formula ⊢ IsAxiom (P.imp_ ((P.imp_ P).imp_ P))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a P : Formula ⊢ IsAxiom (P.imp_ ((P.imp_ P).imp_ P)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	apply IsDeduct.axiom_	case a P : Formula ⊢ IsDeduct ∅ (P.imp_ (P.imp_ P))	case a.a P : Formula ⊢ IsAxiom (P.imp_ (P.imp_ P))	Please generate a tactic in lean4 to solve the state. STATE: case a P : Formula ⊢ IsDeduct ∅ (P.imp_ (P.imp_ P)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_5	[253, 1]	[265, 30]	exact IsAxiom.prop_1_ P P	case a.a P : Formula ⊢ IsAxiom (P.imp_ (P.imp_ P))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a P : Formula ⊢ IsAxiom (P.imp_ (P.imp_ P)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.mp_ (P.not_.imp_ (Q.not_.imp_ P.not_))	P Q : Formula ⊢ IsProof (P.not_.imp_ (P.imp_ Q))	case a P Q : Formula ⊢ IsDeduct ∅ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q))) case a P Q : Formula ⊢ IsDeduct ∅ (P.not_.imp_ (Q.not_.imp_ P.not_))	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula ⊢ IsProof (P.not_.imp_ (P.imp_ Q)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.mp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)))	case a P Q : Formula ⊢ IsDeduct ∅ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q)))	case a.a P Q : Formula ⊢ IsDeduct ∅ ((P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))).imp_ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q)))) case a.a P Q : Formula ⊢ IsDeduct ∅ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)))	Please generate a tactic in lean4 to solve the state. STATE: case a P Q : Formula ⊢ IsDeduct ∅ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.axiom_	case a.a P Q : Formula ⊢ IsDeduct ∅ ((P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))).imp_ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q))))	case a.a.a P Q : Formula ⊢ IsAxiom ((P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))).imp_ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q))))	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula ⊢ IsDeduct ∅ ((P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))).imp_ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q)))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsAxiom.prop_2_	case a.a.a P Q : Formula ⊢ IsAxiom ((P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))).imp_ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q))))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a P Q : Formula ⊢ IsAxiom ((P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))).imp_ ((P.not_.imp_ (Q.not_.imp_ P.not_)).imp_ (P.not_.imp_ (P.imp_ Q)))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.mp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))	case a.a P Q : Formula ⊢ IsDeduct ∅ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)))	case a.a.a P Q : Formula ⊢ IsDeduct ∅ (((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)).imp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)))) case a.a.a P Q : Formula ⊢ IsDeduct ∅ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula ⊢ IsDeduct ∅ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.axiom_	case a.a.a P Q : Formula ⊢ IsDeduct ∅ (((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)).imp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))))	case a.a.a.a P Q : Formula ⊢ IsAxiom (((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)).imp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))))	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a P Q : Formula ⊢ IsDeduct ∅ (((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)).imp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsAxiom.prop_1_	case a.a.a.a P Q : Formula ⊢ IsAxiom (((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)).imp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a.a P Q : Formula ⊢ IsAxiom (((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)).imp_ (P.not_.imp_ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.axiom_	case a.a.a P Q : Formula ⊢ IsDeduct ∅ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))	case a.a.a.a P Q : Formula ⊢ IsAxiom ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a P Q : Formula ⊢ IsDeduct ∅ ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsAxiom.prop_3_	case a.a.a.a P Q : Formula ⊢ IsAxiom ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a.a.a P Q : Formula ⊢ IsAxiom ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsDeduct.axiom_	case a P Q : Formula ⊢ IsDeduct ∅ (P.not_.imp_ (Q.not_.imp_ P.not_))	case a.a P Q : Formula ⊢ IsAxiom (P.not_.imp_ (Q.not_.imp_ P.not_))	Please generate a tactic in lean4 to solve the state. STATE: case a P Q : Formula ⊢ IsDeduct ∅ (P.not_.imp_ (Q.not_.imp_ P.not_)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_13_6_no_deduct	[270, 1]	[284, 26]	apply IsAxiom.prop_1_	case a.a P Q : Formula ⊢ IsAxiom (P.not_.imp_ (Q.not_.imp_ P.not_))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula ⊢ IsAxiom (P.not_.imp_ (Q.not_.imp_ P.not_)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	intro Γ	F : Formula Δ : Set Formula h1 : IsDeduct Δ F ⊢ ∀ (Γ : Set Formula), IsDeduct (Δ ∪ Γ) F	F : Formula Δ : Set Formula h1 : IsDeduct Δ F Γ : Set Formula ⊢ IsDeduct (Δ ∪ Γ) F	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ : Set Formula h1 : IsDeduct Δ F ⊢ ∀ (Γ : Set Formula), IsDeduct (Δ ∪ Γ) F TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	induction h1	F : Formula Δ : Set Formula h1 : IsDeduct Δ F Γ : Set Formula ⊢ IsDeduct (Δ ∪ Γ) F	case axiom_ F : Formula Δ Γ : Set Formula phi✝ : Formula a✝ : IsAxiom phi✝ ⊢ IsDeduct (Δ ∪ Γ) phi✝ case assume_ F : Formula Δ Γ : Set Formula phi✝ : Formula a✝ : phi✝ ∈ Δ ⊢ IsDeduct (Δ ∪ Γ) phi✝ case mp_ F : Formula Δ Γ : Set Formula phi✝ psi✝ : Formula a✝¹ : IsDeduct Δ (phi✝.imp_ psi✝) a✝ : IsDeduct Δ phi✝ a_ih✝¹ : ...	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ : Set Formula h1 : IsDeduct Δ F Γ : Set Formula ⊢ IsDeduct (Δ ∪ Γ) F TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	case axiom_ h1_phi h1_1 => apply IsDeduct.axiom_ exact h1_1	F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_phi	no goals	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	case assume_ h1_phi h1_1 => apply IsDeduct.assume_ simp left exact h1_1	F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct (Δ ∪ Γ) h1_phi	no goals	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct (Δ ∪ Γ) h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	apply IsDeduct.axiom_	F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_phi	case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	exact h1_1	case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	apply IsDeduct.assume_	F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct (Δ ∪ Γ) h1_phi	case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ ∪ Γ	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct (Δ ∪ Γ) h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	simp	case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ ∪ Γ	case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ ∨ h1_phi ∈ Γ	Please generate a tactic in lean4 to solve the state. STATE: case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ ∪ Γ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	left	case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ ∨ h1_phi ∈ Γ	case a.h F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ	Please generate a tactic in lean4 to solve the state. STATE: case a F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ ∨ h1_phi ∈ Γ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	exact h1_1	case a.h F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.h F : Formula Δ Γ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	apply IsDeduct.mp_ h1_phi	F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_psi	case a F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) case a F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct...	Please generate a tactic in lean4 to solve the state. STATE: F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_psi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	exact h1_ih_1	case a F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi)	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10	[287, 1]	[306, 20]	exact h1_ih_2	case a F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_phi	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a F : Formula Δ Γ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct (Δ ∪ Γ) (h1_phi.imp_ h1_psi) h1_ih_2 : IsDeduct (Δ ∪ Γ) h1_phi ⊢ IsDeduct (Δ ∪ Γ) h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10_comm	[309, 1]	[316, 23]	simp only [Set.union_comm]	Q : Formula Δ : Set Formula h1 : IsDeduct Δ Q ⊢ ∀ (Γ : Set Formula), IsDeduct (Γ ∪ Δ) Q	Q : Formula Δ : Set Formula h1 : IsDeduct Δ Q ⊢ ∀ (Γ : Set Formula), IsDeduct (Δ ∪ Γ) Q	Please generate a tactic in lean4 to solve the state. STATE: Q : Formula Δ : Set Formula h1 : IsDeduct Δ Q ⊢ ∀ (Γ : Set Formula), IsDeduct (Γ ∪ Δ) Q TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_10_comm	[309, 1]	[316, 23]	exact T_14_10 Q Δ h1	Q : Formula Δ : Set Formula h1 : IsDeduct Δ Q ⊢ ∀ (Γ : Set Formula), IsDeduct (Δ ∪ Γ) Q	no goals	Please generate a tactic in lean4 to solve the state. STATE: Q : Formula Δ : Set Formula h1 : IsDeduct Δ Q ⊢ ∀ (Γ : Set Formula), IsDeduct (Δ ∪ Γ) Q TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.C_14_11	[319, 1]	[327, 11]	intro Δ	P : Formula h1 : IsProof P ⊢ ∀ (Δ : Set Formula), IsDeduct Δ P	P : Formula h1 : IsProof P Δ : Set Formula ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : IsProof P ⊢ ∀ (Δ : Set Formula), IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.C_14_11	[319, 1]	[327, 11]	obtain s1 := T_14_10 P ∅ h1 Δ	P : Formula h1 : IsProof P Δ : Set Formula ⊢ IsDeduct Δ P	P : Formula h1 : IsProof P Δ : Set Formula s1 : IsDeduct (∅ ∪ Δ) P ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : IsProof P Δ : Set Formula ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.C_14_11	[319, 1]	[327, 11]	simp at s1	P : Formula h1 : IsProof P Δ : Set Formula s1 : IsDeduct (∅ ∪ Δ) P ⊢ IsDeduct Δ P	P : Formula h1 : IsProof P Δ : Set Formula s1 : IsDeduct Δ P ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : IsProof P Δ : Set Formula s1 : IsDeduct (∅ ∪ Δ) P ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.C_14_11	[319, 1]	[327, 11]	exact s1	P : Formula h1 : IsProof P Δ : Set Formula s1 : IsDeduct Δ P ⊢ IsDeduct Δ P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula h1 : IsProof P Δ : Set Formula s1 : IsDeduct Δ P ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	induction h1	P Q : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {P}) Q ⊢ IsDeduct Δ (P.imp_ Q)	case axiom_ P Q : Formula Δ : Set Formula phi✝ : Formula a✝ : IsAxiom phi✝ ⊢ IsDeduct Δ (P.imp_ phi✝) case assume_ P Q : Formula Δ : Set Formula phi✝ : Formula a✝ : phi✝ ∈ Δ ∪ {P} ⊢ IsDeduct Δ (P.imp_ phi✝) case mp_ P Q : Formula Δ : Set Formula phi✝ psi✝ : Formula a✝¹ : IsDeduct (Δ ∪ {P}) (phi✝.imp_ psi✝) a✝ : IsDed...	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {P}) Q ⊢ IsDeduct Δ (P.imp_ Q) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.mp_ h1_phi	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (P.imp_ h1_phi)	case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi)) case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ h1_phi	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (P.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.axiom_	case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi))	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi))	Please generate a tactic in lean4 to solve the state. STATE: case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	exact IsAxiom.prop_1_ h1_phi P	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.axiom_	case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ h1_phi	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi	Please generate a tactic in lean4 to solve the state. STATE: case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	exact h1_1	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	simp at h1_1	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ∪ {P} ⊢ IsDeduct Δ (P.imp_ h1_phi)	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ∨ h1_phi ∈ Δ ⊢ IsDeduct Δ (P.imp_ h1_phi)	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ∪ {P} ⊢ IsDeduct Δ (P.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	cases h1_1	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ∨ h1_phi ∈ Δ ⊢ IsDeduct Δ (P.imp_ h1_phi)	case inl P Q : Formula Δ : Set Formula h1_phi : Formula h✝ : h1_phi = P ⊢ IsDeduct Δ (P.imp_ h1_phi) case inr P Q : Formula Δ : Set Formula h1_phi : Formula h✝ : h1_phi ∈ Δ ⊢ IsDeduct Δ (P.imp_ h1_phi)	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ∨ h1_phi ∈ Δ ⊢ IsDeduct Δ (P.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	case inl h1_1 => subst h1_1 apply proof_imp_deduct exact prop_id h1_phi	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ⊢ IsDeduct Δ (P.imp_ h1_phi)	no goals	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ⊢ IsDeduct Δ (P.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	subst h1_1	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ⊢ IsDeduct Δ (P.imp_ h1_phi)	Q : Formula Δ : Set Formula h1_phi : Formula ⊢ IsDeduct Δ (h1_phi.imp_ h1_phi)	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi = P ⊢ IsDeduct Δ (P.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply proof_imp_deduct	Q : Formula Δ : Set Formula h1_phi : Formula ⊢ IsDeduct Δ (h1_phi.imp_ h1_phi)	case h1 Q : Formula Δ : Set Formula h1_phi : Formula ⊢ IsProof (h1_phi.imp_ h1_phi)	Please generate a tactic in lean4 to solve the state. STATE: Q : Formula Δ : Set Formula h1_phi : Formula ⊢ IsDeduct Δ (h1_phi.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	exact prop_id h1_phi	case h1 Q : Formula Δ : Set Formula h1_phi : Formula ⊢ IsProof (h1_phi.imp_ h1_phi)	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h1 Q : Formula Δ : Set Formula h1_phi : Formula ⊢ IsProof (h1_phi.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.mp_ h1_phi	P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (P.imp_ h1_phi)	case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi)) case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ h1_phi	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (P.imp_ h1_phi) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.axiom_	case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi))	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi))	Please generate a tactic in lean4 to solve the state. STATE: case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	exact IsAxiom.prop_1_ h1_phi P	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.assume_	case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ h1_phi	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ	Please generate a tactic in lean4 to solve the state. STATE: case a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ h1_phi TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	exact h1_1	case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a P Q : Formula Δ : Set Formula h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_3	[333, 1]	[366, 20]	apply IsDeduct.mp_ (P.imp_ h1_phi)	P Q : Formula Δ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi) a✝ : IsDeduct (Δ ∪ {P}) h1_phi h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi) ⊢ IsDeduct Δ (P.imp_ h1_psi)	case a P Q : Formula Δ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi) a✝ : IsDeduct (Δ ∪ {P}) h1_phi h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi) ⊢ IsDeduct Δ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi)) case a P Q : Formula Δ : Set Formula h1_p...	Please generate a tactic in lean4 to solve the state. STATE: P Q : Formula Δ : Set Formula h1_phi h1_psi : Formula a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi) a✝ : IsDeduct (Δ ∪ {P}) h1_phi h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi) ⊢ IsDeduct Δ (P.imp_ h1_psi) TACTIC:

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.