induction s <;> try simp [Rew.func, bv_func, Finset.biUnion_biUnion, *]
L : Language
ξ : Type u_1
n k : ℕ
o : Operator L k
v : Fin k → Semiterm L ξ (n + 1)
s : Semiterm L Empty k
⊢ ((Rew.substs v) (Rew.emb s)).bv = s.bv.biUnion fun i => (v i).bv
case fvar
L : Language
ξ : Type u_1
n k : ℕ
o : Operator L k
v : Fin k → Semiterm L ξ (n + 1)
a✝ : Empty
⊢ ((Rew.substs v) (Rew.emb &a✝)).bv = ∅