diff --git a/theories/decidable.v b/theories/decidable.v
index 310eff9a1803fce53454c1195323f7cf206b0680..89b74b2e74aec5081614b8d613007a5ffedc3d99 100644
--- a/theories/decidable.v
+++ b/theories/decidable.v
@@ -25,9 +25,9 @@ Lemma decide_iff {A} P Q `{Decision P, Decision Q} (x y : A) :
   (P ↔ Q) → (if decide P then x else y) = (if decide Q then x else y).
 Proof. intros [??]. destruct (decide P), (decide Q); tauto. Qed.
 
-Lemma decide_left `{Decision P, !ProofIrrel P} (HP : P) : decide P = left HP.
+Lemma decide_True_pi `{Decision P, !ProofIrrel P} (HP : P) : decide P = left HP.
 Proof. destruct (decide P); [|contradiction]. f_equal. apply proof_irrel. Qed.
-Lemma decide_right `{Decision P, !ProofIrrel (¬ P)} (HP : ¬ P) : decide P = right HP.
+Lemma decide_False_pi `{Decision P, !ProofIrrel (¬ P)} (HP : ¬ P) : decide P = right HP.
 Proof. destruct (decide P); [contradiction|]. f_equal. apply proof_irrel. Qed.
 
 (** The tactic [destruct_decide] destructs a sumbool [dec]. If one of the