have d₁ : T ⊢! ⦍β⦎κ(σ) ⟶ σ := imp_trans! (Subtheory.prf! (kreisel_specAux₁ σ)) H
L : Language
inst✝⁴ : DecidableEq (Sentence L)
inst✝³ : Semiterm.Operator.GoedelNumber L (Sentence L)
T₀ T : Theory L
inst✝² : T₀ ≼ T
inst✝¹ : Diagonalization T₀
β : ProvabilityPredicate L L
inst✝ : β.HilbertBernays T₀ T
σ : Sentence L
H : T ⊢! ⦍β⦎σ ⟶ σ
⊢ T ⊢! σ
L : Language
inst✝⁴ : DecidableEq (Sentence L)
inst✝³ : Semiterm.Operator.GoedelNumber L (Sentence L)
T₀ T : Theory L
inst✝² : T₀ ≼ T
inst✝¹ : Diagonalization T₀
β : ProvabilityPredicate L L
inst✝ : β.HilbertBernays T₀ T
σ : Sentence L
H : T ⊢! ⦍β⦎σ ⟶ σ
d₁ : T ⊢! ⦍β⦎κ(σ) ⟶ σ
⊢ T ⊢! σ