intro h s₁ hs₁
case mp
L L₁ L₂ : Language
Φ : L₁ →ᵥ L₂
injf : ∀ (k : ℕ), Function.Injective Φ.func
injr : ∀ (k : ℕ), Function.Injective Φ.rel
T : Theory L₁
σ : Sentence L₁
⊢ Theory.lMap Φ T ⊨ (Semiformula.lMap Φ) σ → T ⊨ σ
case mp
L L₁ L₂ : Language
Φ : L₁ →ᵥ L₂
injf : ∀ (k : ℕ), Function.Injective Φ.func
injr : ∀ (k : ℕ), Function.Injective Φ.rel
T : Theory L₁
σ : Sentence L₁
h : Theory.lMap Φ T ⊨ (Semiformula.lMap Φ) σ
s₁ : SmallStruc L₁
hs₁ : s₁ ∈ Semantics.models (SmallStruc L₁) T
⊢ s₁ ⊧ σ