subst_vars
case hMaxm.inl.intro.intro
α : Type u_1
inst✝⁵ : DecidableEq α
L : Language
inst✝⁴ : Semiterm.Operator.GoedelNumber L (Sentence L)
inst✝³ : DecidableEq (Sentence L)
T₀ T : FirstOrder.Theory L
inst✝² : T₀ ≼ T
inst✝¹ : Diagonalization T₀
β : ProvabilityPredicate L L
inst✝ : β.HilbertBernays T₀ T
p✝¹ : Formula α
f : realization L α
p✝ p q : Formula α
e : Axioms.K p q = p✝
⊢ T ⊢! f[β] p✝
case hMaxm.inl.intro.intro
α : Type u_1
inst✝⁵ : DecidableEq α
L : Language
inst✝⁴ : Semiterm.Operator.GoedelNumber L (Sentence L)
inst✝³ : DecidableEq (Sentence L)
T₀ T : FirstOrder.Theory L
inst✝² : T₀ ≼ T
inst✝¹ : Diagonalization T₀
β : ProvabilityPredicate L L
inst✝ : β.HilbertBernays T₀ T
p✝ : Formula α
f : realization L α
p q : Formula α
⊢ T ⊢! f[β] Axioms.K p q