have := this.not_con
α : Type u_1
Δ : Sequent α
T : Theory α
consisT : Consistent T
p q : Formula α
h : p ⋎ q ∈ maximalConsistentTheory consisT
A : ¬(p ∈ maximalConsistentTheory consisT ∨ q ∈ maximalConsistentTheory consisT)
b : maximalConsistentTheory consisT ⊢! ~p ∧ maximalConsistentTheory consisT ⊢! ~q
this : Inconsistent (maximalConsistentTheory consisT)
⊢ False
α : Type u_1
Δ : Sequent α
T : Theory α
consisT : Consistent T
p q : Formula α
h : p ⋎ q ∈ maximalConsistentTheory consisT
A : ¬(p ∈ maximalConsistentTheory consisT ∨ q ∈ maximalConsistentTheory consisT)
b : maximalConsistentTheory consisT ⊢! ~p ∧ maximalConsistentTheory consisT ⊢! ~q
this✝ : Inconsistent (maximalConsistentTheory consisT)
this : ¬Consistent (maximalConsistentTheory consisT)
⊢ False