proposition: Lemma dec_eq_uip' {U x y} (pf : x = y) (p : forall y : U, {x = y} + {x <> y}) : pf = match dec_eq_adjust' p y with | left pf' => pf' | right pf' => match pf' pf with end end.
proof: Proof. destruct pf. unfold dec_eq_adjust'. destruct (p x) as [|n]. { symmetry; apply concat_Vp. } { destruct (n eq_refl). } Defined.
imports: Coq.Logic.EqdepFacts Fiat.Common.Coq__8_4__8_5__Compat