simp [lindenbaum_next_indexed, lindenbaum_next]
α : Type u_1
inst✝⁴ : DecidableEq α
inst✝³ : Inhabited α
𝓓 : DeductionParameter α
inst✝² : 𝓓.IncludeEFQ
inst✝¹ : Inhabited α
inst✝ : Encodable α
t✝ t : Tableau α
p : Formula α
⊢ p ∈ t[encode p + 1].1 ∨ p ∈ t[encode p + 1].2
α : Type u_1
inst✝⁴ : DecidableEq α
inst✝³ : Inhabited α
𝓓 : DeductionParameter α
inst✝² : 𝓓.IncludeEFQ
inst✝¹ : Inhabited α
inst✝ : Encodable α
t✝ t : Tableau α
p : Formula α
⊢ p ∈
      (if (𝓓)-Consistent (insert p t[encode p].1, t[encode p].2) then (insert p t[encode p].1, t[encode p].2)
        else (t[encode p].1, insert p t[encode p].2)).1 ∨
    p ∈
      (if (𝓓)-Consistent (insert p t[encode p].1, t[encode p].2) then (insert p t[encode p].1, t[encode p].2)
        else (t[encode p].1, insert p t[encode p].2)).2