left
case inl
α : Type u_1
Δ : Sequent α
T : Theory α
consisT : Consistent T
p q : Formula α
ihp : p ∈ maximalConsistentTheory consisT → { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ p
ihq : q ∈ maximalConsistentTheory consisT → { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ q
hp✝ : p ⋎ q ∈ maximalConsistentTheory consisT
hp : p ∈ maximalConsistentTheory consisT
⊢ { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ p ∨
    { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ q
case inl.h
α : Type u_1
Δ : Sequent α
T : Theory α
consisT : Consistent T
p q : Formula α
ihp : p ∈ maximalConsistentTheory consisT → { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ p
ihq : q ∈ maximalConsistentTheory consisT → { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ q
hp✝ : p ⋎ q ∈ maximalConsistentTheory consisT
hp : p ∈ maximalConsistentTheory consisT
⊢ { val := fun x => Formula.atom x ∈ maximalConsistentTheory consisT } ⊧ p