intro c hc chain hnc
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
consisT : (L)-Consistent T
⊢ ∀ c ⊆ {T | (L)-Consistent T},
    IsChain (fun x x_1 => x ⊆ x_1) c → c.Nonempty → ∃ ub ∈ {T | (L)-Consistent T}, ∀ s ∈ c, s ⊆ ub
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
consisT : (L)-Consistent T
c : Set (Set (Formula α))
hc : c ⊆ {T | (L)-Consistent T}
chain : IsChain (fun x x_1 => x ⊆ x_1) c
hnc : c.Nonempty
⊢ ∃ ub ∈ {T | (L)-Consistent T}, ∀ s ∈ c, s ⊆ ub