induction Γ using List.induction_with_singleton with
| hnil => simp_all only [List.conj'_nil, IsEmpty.forall_iff, forall_const]; exact dhyp! $ verum!;
| hsingle => simp_all only [List.mem_singleton, forall_eq, List.conj'_singleton, imp_id!];
| hcons r Γ h ih =>
  simp [List.conj'_cons_nonempty h];
  simp at he;
  have ⟨he₁, he₂⟩ := he;
  subst he₁;
  exact implyRightAnd! imp_id! (ih he₂);
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
he : ∀ g ∈ Γ, g = p
⊢ 𝓢 ⊢! p ⟶ Γ.conj'
no goals