simp[hU, hl, hproper, this]
case h
μ : Type ?u.1169140
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
l : ProofList L
U : List (Sentence L)
hU : ∀ x ∈ U, T x
hl : Rew.emb.hom σ :: List.map (⇑Rew.emb.hom ∘ fun x => ~x) U ∈ l.sequents
hproper : l.isProper = true
this : (U.all fun x => decide (T x)) = true
⊢ Option.rec false
      (fun val =>
        (val.2.all fun x => decide (T x)) &&
            decide (Rew.emb.hom σ :: List.map (⇑Rew.emb.hom ∘ fun x => ~x) val.2 ∈ val.1.sequents) &&
          val.1.isProper)
      ((decode (encode (l, U)).unpair.1).bind fun a => Option.map (Prod.mk a) (decode (encode (l, U)).unpair.2)) =
    true
no goals