diff options
| -rw-r--r-- | doc/changelog/10-standard-library/13365-axiom-free-wf.rst | 4 | ||||
| -rw-r--r-- | theories/Program/Wf.v | 5 |
2 files changed, 6 insertions, 3 deletions
diff --git a/doc/changelog/10-standard-library/13365-axiom-free-wf.rst b/doc/changelog/10-standard-library/13365-axiom-free-wf.rst new file mode 100644 index 0000000000..1fc40894eb --- /dev/null +++ b/doc/changelog/10-standard-library/13365-axiom-free-wf.rst @@ -0,0 +1,4 @@ +- **Fixed:** + `Coq.Program.Wf.Fix_F_inv` and `Coq.Program.Wf.Fix_eq` are now axiom-free. They no longer assume proof irrelevance. + (`#13365 <https://github.com/coq/coq/pull/13365>`_, + by Li-yao Xia). diff --git a/theories/Program/Wf.v b/theories/Program/Wf.v index 50351d6a14..688db8b812 100644 --- a/theories/Program/Wf.v +++ b/theories/Program/Wf.v @@ -12,8 +12,6 @@ Require Import Coq.Init.Wf. Require Import Coq.Program.Utils. -Require Import ProofIrrelevance. -Require Import FunctionalExtensionality. Local Open Scope program_scope. @@ -51,7 +49,7 @@ Section Well_founded. Lemma Fix_F_inv : forall (x:A) (r s:Acc R x), Fix_F_sub x r = Fix_F_sub x s. Proof. intro x; induction (Rwf x); intros. - rewrite (proof_irrelevance (Acc R x) r s) ; auto. + rewrite <- 2 Fix_F_eq; intros. apply F_ext; intros []; auto. Qed. Lemma Fix_eq : forall x:A, Fix_sub x = F_sub x (fun y:{ y:A | R y x} => Fix_sub (proj1_sig y)). @@ -226,6 +224,7 @@ Ltac fold_sub f := (** This module provides the fixpoint equation provided one assumes functional extensionality. *) +Require Import FunctionalExtensionality. Module WfExtensionality. |