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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
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp	case a Δ_U : Set Formula V : VarBoolAssignment X : PredName xs : List VarName F : Formula := pred_var_ X xs h1 : pred_var_ X xs ∈ Δ_U ⊢ (if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U	case a Δ_U : Set Formula V : VarBoolAssignment X : PredName xs : List VarName F : Formula := pred_var_ X xs h1 : pred_var_ X xs ∈ Δ_U ⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply Exists.intro F	case a Δ_U : Set Formula V : VarBoolAssignment X : PredName xs : List VarName F : Formula := pred_var_ X xs h1 : pred_var_ X xs ∈ Δ_U ⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_	case a Δ_U : Set Formula V : VarBoolAssignment X : PredName xs : List VarName F : Formula := pred_var_ X xs h1 : pred_var_ X xs ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	tauto	case a Δ_U : Set Formula V : VarBoolAssignment X : PredName xs : List VarName F : Formula := pred_var_ X xs h1 : pred_var_ X xs ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	let F := eq_ x y	Δ_U : Set Formula V : VarBoolAssignment x y : VarName h1 : ↑(eq_ x y).primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))	Δ_U : Set Formula V : VarBoolAssignment x y : VarName h1 : ↑(eq_ x y).primeSet ⊆ Δ_U F : Formula := eq_ x y ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.primeSet] at h1	Δ_U : Set Formula V : VarBoolAssignment x y : VarName h1 : ↑(eq_ x y).primeSet ⊆ Δ_U F : Formula := eq_ x y ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))	Δ_U : Set Formula V : VarBoolAssignment x y : VarName h1 : ↑{eq_ x y} ⊆ Δ_U F : Formula := eq_ x y ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at h1	Δ_U : Set Formula V : VarBoolAssignment x y : VarName h1 : ↑{eq_ x y} ⊆ Δ_U F : Formula := eq_ x y ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))	Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot]	Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))	Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (eq_ x y) then eq_ x y else (eq_ x y).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.evalPrime]	Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (eq_ x y) then eq_ x y else (eq_ x y).not_)	Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.assume_	Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_)	case a Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp	case a Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ (if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U	case a Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply Exists.intro F	case a Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_	case a Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	tauto	case a Δ_U : Set Formula V : VarBoolAssignment x y : VarName F : Formula := eq_ x y h1 : eq_ x y ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (eq_ x y) = true then eq_ x y else (eq_ x y).not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.axiom_	Δ_U : Set Formula V : VarBoolAssignment h1 : ↑true_.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V true_)	case a Δ_U : Set Formula V : VarBoolAssignment h1 : ↑true_.primeSet ⊆ Δ_U ⊢ IsAxiom (evalPrimeFfToNot V true_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsAxiom.prop_true_	case a Δ_U : Set Formula V : VarBoolAssignment h1 : ↑true_.primeSet ⊆ Δ_U ⊢ IsAxiom (evalPrimeFfToNot V true_)	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.primeSet] at h1	Δ_U : Set Formula V : VarBoolAssignment h1 : ↑false_.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)	Δ_U : Set Formula V : VarBoolAssignment h1 : ↑∅ ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at h1	Δ_U : Set Formula V : VarBoolAssignment h1 : ↑∅ ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot]	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V false_ then false_ else false_.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.evalPrime]	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V false_ then false_ else false_.not_)	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then false_ else false_.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then false_ else false_.not_)	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) false_.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	sorry	Δ_U : Set Formula V : VarBoolAssignment h1 : True ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) false_.not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.primeSet] at h1	Δ_U : Set Formula V : VarBoolAssignment phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑phi.not_.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)	Δ_U : Set Formula V : VarBoolAssignment phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑phi.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot] at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑phi.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot]	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi.not_ then phi.not_ else phi.not_.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrime]	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi.not_ then phi.not_ else phi.not_.not_)	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if ¬evalPrime V phi then phi.not_ else phi.not_.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if ¬evalPrime V phi then phi.not_ else phi.not_.not_)	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi.not_.not_ else phi.not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	split_ifs	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi.not_.not_ else phi.not_)	case pos Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h✝ : evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_ case neg Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h✝ : ¬evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	case _ c1 => simp only [c1] at phi_ih simp at phi_ih apply IsDeduct.mp_ phi apply proof_imp_deduct apply T_14_6 exact phi_ih h1	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) c1 : evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	case _ c1 => simp only [c1] at phi_ih simp at phi_ih exact phi_ih h1	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) c1 : ¬evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [c1] at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) c1 : evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if True then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if True then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.mp_ phi	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_.not_	case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ phi.not_.not_) case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply proof_imp_deduct	case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ phi.not_.not_) case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi	case a.h1 Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsProof (phi.imp_ phi.not_.not_) case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply T_14_6	case a.h1 Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsProof (phi.imp_ phi.not_.not_) case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi	case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	exact phi_ih h1	case a Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [c1] at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) c1 : ¬evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if False then phi else phi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	exact phi_ih h1	Δ_U : Set Formula V : VarBoolAssignment phi : Formula h1 : ↑phi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.primeSet] at h1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑(phi.imp_ psi).primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑(phi.primeSet ∪ psi.primeSet) ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at h1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑(phi.primeSet ∪ psi.primeSet) ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot] at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot] at psi_ih	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V psi) h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot]	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (phi.imp_ psi))	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (phi.imp_ psi) then phi.imp_ psi else (phi.imp_ psi).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	cases h1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1 : ↑phi.primeSet ⊆ Δ_U ∧ ↑psi.primeSet ⊆ Δ_U phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (phi.imp_ psi) then phi.imp_ psi else (phi.imp_ psi).not_)	case intro Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) left✝ : ↑phi.primeSet ⊆ Δ_U right✝ : ↑psi.primeSet ⊆ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (phi.imp_ psi) then phi.imp_ psi else (phi.imp_ psi).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	split_ifs	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (phi.imp_ psi) then phi.imp_ psi else (phi.imp_ psi).not_)	case pos Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U h✝ : evalPrime V (phi.imp_ psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi) case neg Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U h✝ : ¬evalPrime V (phi.imp_ psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	case _ c1 => simp only [evalPrime] at c1 simp only [imp_iff_not_or] at c1 cases c1 case _ c1 => simp only [if_neg c1] at phi_ih apply IsDeduct.mp_ (not_ phi) apply proof_imp_deduct apply T_13_6 apply phi_ih h1_left case _ c1 => simp only [if_pos c1] at psi_ih apply IsDeduct.mp_ psi apply IsDeduct.axiom_ apply IsAxiom.prop_1_ apply psi_ih exact h1_right	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V (phi.imp_ psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrime] at c1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V (phi.imp_ psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V phi → evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [imp_iff_not_or] at c1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V phi → evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi ∨ evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	cases c1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi ∨ evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	case inl Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U h✝ : ¬evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi) case inr Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U h✝ : evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	case _ c1 => simp only [if_neg c1] at phi_ih apply IsDeduct.mp_ (not_ phi) apply proof_imp_deduct apply T_13_6 apply phi_ih h1_left	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	case _ c1 => simp only [if_pos c1] at psi_ih apply IsDeduct.mp_ psi apply IsDeduct.axiom_ apply IsAxiom.prop_1_ apply psi_ih exact h1_right	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [if_neg c1] at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.mp_ (not_ phi)	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.not_.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply proof_imp_deduct	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.not_.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	case a.h1 Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsProof (phi.not_.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply T_13_6	case a.h1 Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsProof (phi.not_.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply phi_ih h1_left	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V phi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi.not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [if_pos c1] at psi_ih	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.mp_ psi	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi)	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (psi.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.axiom_	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (psi.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi	case a.a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsAxiom (psi.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsAxiom.prop_1_	case a.a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsAxiom (psi.imp_ (phi.imp_ psi)) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply psi_ih	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ ↑psi.primeSet ⊆ Δ_U
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	exact h1_right	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V psi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi ⊢ ↑psi.primeSet ⊆ Δ_U	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrime] at c1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬evalPrime V (phi.imp_ psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬(evalPrime V phi → evalPrime V psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at c1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : ¬(evalPrime V phi → evalPrime V psi) ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V phi ∧ ¬evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	cases c1	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1 : evalPrime V phi ∧ ¬evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_	case intro Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U left✝ : evalPrime V phi right✝ : ¬evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [if_pos c1_left] at phi_ih	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V phi then phi else phi.not_) psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [if_neg c1_right] at psi_ih	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V psi then psi else psi.not_) h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.mp_ psi.not_	Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ psi).not_	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (psi.not_.imp_ (phi.imp_ psi).not_) case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.mp_ phi	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (psi.not_.imp_ (phi.imp_ psi).not_)	case a.a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ (psi.not_.imp_ (phi.imp_ psi).not_)) case a.a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply proof_imp_deduct	case a.a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (phi.imp_ (psi.not_.imp_ (phi.imp_ psi).not_))	case a.a.h1 Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsProof (phi.imp_ (psi.not_.imp_ (phi.imp_ psi).not_))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply T_14_8	case a.a.h1 Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsProof (phi.imp_ (psi.not_.imp_ (phi.imp_ psi).not_))	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	exact phi_ih h1_left	case a.a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	exact psi_ih h1_right	case a Δ_U : Set Formula V : VarBoolAssignment phi psi : Formula h1_left : ↑phi.primeSet ⊆ Δ_U h1_right : ↑psi.primeSet ⊆ Δ_U c1_left : evalPrime V phi c1_right : ¬evalPrime V psi phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) phi psi_ih : ↑psi.primeSet ⊆ Δ_U → IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_ ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) psi.not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	let F := forall_ x phi	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U F : Formula := forall_ x phi ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.primeSet] at h1	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U F : Formula := forall_ x phi ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑{forall_ x phi} ⊆ Δ_U F : Formula := forall_ x phi ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at h1	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) h1 : ↑{forall_ x phi} ⊆ Δ_U F : Formula := forall_ x phi ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot]	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (forall_ x phi) then forall_ x phi else (forall_ x phi).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.evalPrime]	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (forall_ x phi) then forall_ x phi else (forall_ x phi).not_)	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.assume_	Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_)	case a Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ (if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp	case a Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ (if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U	case a Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply Exists.intro F	case a Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ ∃ x_1 ∈ Δ_U, (if evalPrime V x_1 then x_1 else x_1.not_) = if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_	case a Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	tauto	case a Δ_U : Set Formula V : VarBoolAssignment x : VarName phi : Formula phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi) F : Formula := forall_ x phi h1 : forall_ x phi ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (forall_ x phi) = true then forall_ x phi else (forall_ x phi).not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	let F := def_ X xs	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName h1 : ↑(def_ X xs).primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName h1 : ↑(def_ X xs).primeSet ⊆ Δ_U F : Formula := def_ X xs ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.primeSet] at h1	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName h1 : ↑(def_ X xs).primeSet ⊆ Δ_U F : Formula := def_ X xs ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName h1 : ↑{def_ X xs} ⊆ Δ_U F : Formula := def_ X xs ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp at h1	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName h1 : ↑{def_ X xs} ⊆ Δ_U F : Formula := def_ X xs ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [evalPrimeFfToNot]	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (def_ X xs) then def_ X xs else (def_ X xs).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp only [Formula.evalPrime]	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if evalPrime V (def_ X xs) then def_ X xs else (def_ X xs).not_)	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply IsDeduct.assume_	Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U) (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_)	case a Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	simp	case a Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ (if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_) ∈ (fun a => if evalPrime V a then a else a.not_) '' Δ_U	case a Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	apply Exists.intro F	case a Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ ∃ x ∈ Δ_U, (if evalPrime V x then x else x.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_	case a Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	tauto	case a Δ_U : Set Formula V : VarBoolAssignment X : DefName xs : List VarName F : Formula := def_ X xs h1 : def_ X xs ∈ Δ_U ⊢ F ∈ Δ_U ∧ (if evalPrime V F then F else F.not_) = if V (def_ X xs) = true then def_ X xs else (def_ X xs).not_	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.L_15_7	[773, 1]	[916, 10]	sorry	Δ_U : Set Formula V : VarBoolAssignment a✝¹ : VarName a✝ : Formula a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝) h1 : ↑(exists_ a✝¹ a✝).primeSet ⊆ Δ_U ⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (exists_ a✝¹ a✝))	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	apply IsDeduct.mp_ (U.not_.imp_ P)	P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ P	case a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ ((U.not_.imp_ P).imp_ P) case a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ (U.not_.imp_ P)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	apply IsDeduct.mp_ (U.imp_ P)	case a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ ((U.not_.imp_ P).imp_ P)	case a.a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P)) case a.a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ (U.imp_ P)
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	apply proof_imp_deduct	case a.a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P))	case a.a.h1 P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsProof ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P))
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	apply T_14_9	case a.a.h1 P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsProof ((U.imp_ P).imp_ ((U.not_.imp_ P).imp_ P))	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	apply deduction_theorem	case a.a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ (U.imp_ P)	case a.a.h1 P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct (Δ ∪ {U}) P
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	exact h1	case a.a.h1 P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct (Δ ∪ {U}) P	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	apply deduction_theorem	case a P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct Δ (U.not_.imp_ P)	case a.h1 P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct (Δ ∪ {U.not_}) P
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.T_14_9_Deduct	[919, 1]	[933, 13]	exact h2	case a.h1 P U : Formula Δ : Set Formula h1 : IsDeduct (Δ ∪ {U}) P h2 : IsDeduct (Δ ∪ {U.not_}) P ⊢ IsDeduct (Δ ∪ {U.not_}) P	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Prop.lean	FOL.NV.evalPrimeFfToNot_of_function_updateIte_true	[936, 1]	[950, 38]	induction F	F F' : Formula V : VarBoolAssignment h1 : F.IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) F = Function.updateITE (evalPrimeFfToNot V) F' F F	case pred_const_ F' : Formula V : VarBoolAssignment a✝¹ : PredName a✝ : List VarName h1 : (pred_const_ a✝¹ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (pred_const_ a✝¹ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (pred_const_ a✝¹ a✝) (pred_const_ a✝¹ a✝) case pred_var_ F' : Formula V : VarBoolAssignment a✝¹ : PredName a✝ : List VarName h1 : (pred_var_ a✝¹ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (pred_var_ a✝¹ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (pred_var_ a✝¹ a✝) (pred_var_ a✝¹ a✝) case eq_ F' : Formula V : VarBoolAssignment a✝¹ a✝ : VarName h1 : (eq_ a✝¹ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (eq_ a✝¹ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (eq_ a✝¹ a✝) (eq_ a✝¹ a✝) case true_ F' : Formula V : VarBoolAssignment h1 : true_.IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) true_ = Function.updateITE (evalPrimeFfToNot V) F' true_ true_ case false_ F' : Formula V : VarBoolAssignment h1 : false_.IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) false_ = Function.updateITE (evalPrimeFfToNot V) F' false_ false_ case not_ F' : Formula V : VarBoolAssignment a✝ : Formula a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : a✝.not_.IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) a✝.not_ = Function.updateITE (evalPrimeFfToNot V) F' a✝.not_ a✝.not_ case imp_ F' : Formula V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝¹ = Function.updateITE (evalPrimeFfToNot V) F' a✝¹ a✝¹ a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : (a✝¹.imp_ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (a✝¹.imp_ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (a✝¹.imp_ a✝) (a✝¹.imp_ a✝) case and_ F' : Formula V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝¹ = Function.updateITE (evalPrimeFfToNot V) F' a✝¹ a✝¹ a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : (a✝¹.and_ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (a✝¹.and_ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (a✝¹.and_ a✝) (a✝¹.and_ a✝) case or_ F' : Formula V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝¹ = Function.updateITE (evalPrimeFfToNot V) F' a✝¹ a✝¹ a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : (a✝¹.or_ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (a✝¹.or_ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (a✝¹.or_ a✝) (a✝¹.or_ a✝) case iff_ F' : Formula V : VarBoolAssignment a✝¹ a✝ : Formula a_ih✝¹ : a✝¹.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝¹ = Function.updateITE (evalPrimeFfToNot V) F' a✝¹ a✝¹ a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : (a✝¹.iff_ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (a✝¹.iff_ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (a✝¹.iff_ a✝) (a✝¹.iff_ a✝) case forall_ F' : Formula V : VarBoolAssignment a✝¹ : VarName a✝ : Formula a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : (forall_ a✝¹ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (forall_ a✝¹ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (forall_ a✝¹ a✝) (forall_ a✝¹ a✝) case exists_ F' : Formula V : VarBoolAssignment a✝¹ : VarName a✝ : Formula a_ih✝ : a✝.IsPrime → evalPrimeFfToNot (Function.updateITE V F' true) a✝ = Function.updateITE (evalPrimeFfToNot V) F' a✝ a✝ h1 : (exists_ a✝¹ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (exists_ a✝¹ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (exists_ a✝¹ a✝) (exists_ a✝¹ a✝) case def_ F' : Formula V : VarBoolAssignment a✝¹ : DefName a✝ : List VarName h1 : (def_ a✝¹ a✝).IsPrime ⊢ evalPrimeFfToNot (Function.updateITE V F' true) (def_ a✝¹ a✝) = Function.updateITE (evalPrimeFfToNot V) F' (def_ a✝¹ a✝) (def_ a✝¹ a✝)

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