rintro ⟨U, hU, d⟩
μ : Type ?u.1107580
L : Language
inst✝⁷ : (k : ℕ) → DecidableEq (L.Func k)
inst✝⁶ : (k : ℕ) → DecidableEq (L.Rel k)
inst✝⁵ : (k : ℕ) → Primcodable (L.Func k)
inst✝⁴ : (k : ℕ) → Primcodable (L.Rel k)
inst✝³ : UniformlyPrimcodable L.Func
inst✝² : UniformlyPrimcodable L.Rel
inst✝¹ : Primcodable μ
T : Theory L
inst✝ : DecidablePred T
σ : Sentence L
⊢ T ⊢! σ →
    ∃ l U,
      (U.all fun x => decide (T x)) = true ∧
        List.map (⇑Rew.emb.hom) (σ :: List.map (fun x => ~x) U) ∈ l.sequents ∧ l.isProper = true
case intro.mk
μ : Type ?u.1107580
L : Language
inst✝⁷ : (k : ℕ) → DecidableEq (L.Func k)
inst✝⁶ : (k : ℕ) → DecidableEq (L.Rel k)
inst✝⁵ : (k : ℕ) → Primcodable (L.Func k)
inst✝⁴ : (k : ℕ) → Primcodable (L.Rel k)
inst✝³ : UniformlyPrimcodable L.Func
inst✝² : UniformlyPrimcodable L.Rel
inst✝¹ : Primcodable μ
T : Theory L
inst✝ : DecidablePred T
σ : Sentence L
U : List (Sentence L)
hU : ∀ p ∈ U, p ∈ T
d : U ⊢² [σ]
⊢ ∃ l U,
    (U.all fun x => decide (T x)) = true ∧
      List.map (⇑Rew.emb.hom) (σ :: List.map (fun x => ~x) U) ∈ l.sequents ∧ l.isProper = true