. intro h;
  apply iff_provable_list_conj.mpr;
  simp only [List.mem_append];
  rintro p (hp₁ | hp₂);
  . exact (iff_provable_list_conj.mp $ conj₁'! h) p hp₁;
  . exact (iff_provable_list_conj.mp $ conj₂'! h) p hp₂;
case mpr
F : Type u_1
inst✝⁴ : LogicalConnective F
inst✝³ : DecidableEq F
S : Type u_2
inst✝² : System F S
𝓢 : S
inst✝¹ : Minimal 𝓢
p q r : F
Γ Δ : List F
inst✝ : System.NegationEquiv 𝓢
⊢ 𝓢 ⊢! Γ.conj' ⋏ Δ.conj' → 𝓢 ⊢! (Γ ++ Δ).conj'
no goals