case ex => rw[length_cast] <;> simp[Rew.q_rewrite, *]
L : Language
Δ Δ₁ Δ₂ Γ : Sequent L
p q r : SyntacticFormula L
Δ✝ : List (SyntacticFormula L)
p✝ : Semiformula L ℕ (Nat.succ 0)
t✝ : Semiterm L ℕ 0
a✝ : Derivation ([→ t✝].hom p✝ :: Δ✝)
a_ih✝ : ∀ (f : ℕ → SyntacticTerm L), length (rewrite a✝ f) = length a✝
f : ℕ → SyntacticTerm L
⊢ length (Derivation.cast (ex ((Rew.rewrite f) t✝) (Derivation.cast (rewrite a✝ f) ⋯)) ⋯) = length a✝ + 1
no goals