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Require Import Ltac2.Ltac2.
Ltac2 congruence_dev () := congruence.
Ltac2 simpl_congruence_dev () := simple congruence.
Lemma congruence_test_1 : (forall x:bool, x = true) -> False.
Proof.
intros.
Fail congruence.
Fail congruence 0 with false.
Fail congruence 1 with true.
congruence 1 with false.
Qed.
Lemma congruence_test_2 : (forall x:bool, x = true) -> False.
Proof.
intros.
Fail congruence.
congruence with false.
Qed.
Lemma congruence_test_3 {A B} (f: A->B->A) (a:A) (b:B): f a b = a -> f (f a b) b = a.
Proof.
congruence.
Qed.
Lemma congruence_test_4 {A} (f: A->A) (a:A): f (f (f a)) = a -> f (f (f (f (f a)))) = a -> f a = a.
Proof.
congruence.
Qed.
Lemma simple_congruence_test_1 : (forall x:bool, x = true) -> False.
Proof.
intros.
Fail simple congruence.
Fail simple congruence 0 with false.
Fail simple congruence 1 with true.
simple congruence 1 with false.
Qed.
Lemma simple_congruence_test_2 : (forall x:bool, x = true) -> False.
Proof.
intros.
Fail simple congruence.
simple congruence with false.
Qed.
Lemma simple_congruence_test_3 {A B} (f: A->B->A) (a:A) (b:B): f a b = a -> f (f a b) b = a.
Proof.
simple congruence.
Qed.
Lemma simple_congruence_test_4 {A} (f: A->A) (a:A): f (f (f a)) = a -> f (f (f (f (f a)))) = a -> f a = a.
Proof.
simple congruence.
Qed.
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