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From Coq.ssr Require Import ssreflect.
From Coq Require Import RelationClasses Relation_Definitions Setoid.
Parameter P : nat -> Prop.
Parameter f : nat -> nat.
Parameter foo_eq : forall x, P 0 -> P 1 -> x = f x.
Axiom p0 : P 0.
Axiom p1 : P 1.
Goal 0 = f 0.
Proof.
rewrite -(foo_eq 0); [ exact: p0 | exact: p1 | reflexivity ].
Abort.
Parameter R : relation nat.
Parameter R_equivalence : Equivalence R.
#[global] Existing Instance R_equivalence.
Parameter foo_R : forall x, P 0 -> P 1 -> R x (f x).
Goal R 0 (f 0).
Proof.
rewrite -(foo_R 0); [ exact: p0 | exact: p1 | apply: Equivalence_Reflexive ].
Abort.
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