intro σ cs₂
Δ✝ : RankedAlphabet
alg₁ alg₂ : Algebra Δ✝
hom : Hom alg₁ alg₂
⊢ Closed alg₂ (Set.image hom.hom)
Δ✝ : RankedAlphabet
alg₁ alg₂ : Algebra Δ✝
hom : Hom alg₁ alg₂
σ : Δ✝.alphabet
cs₂ : { a // Set.image hom.hom a }⋆RankedAlphabet.rank Δ✝ σ
⊢ Algebra.θ alg₂ σ (Vector.lift cs₂) ∈ Set.image hom.hom