Library Axioms
This file collects some axioms used throughout the CompCert development.
Extensionality axioms
Axiom functional_extensionality_dep : forall {A} {B : A -> Type}, forall (f g : forall x : A, B x), (forall x, f x = g x) -> f = g.and, as a corollary, functional extensionality for non-dependent functions:
Lemma functional_extensionality {A B} (f g : A -> B) : (forall x, f x = g x) -> f = g.
For compatibility with earlier developments, extensionality
is an alias for functional_extensionality.
Lemma extensionality:
forall (A B: Type) (f g : A -> B), (forall x, f x = g x) -> f = g.
Proof. intros; apply functional_extensionality. auto. Qed.
Implicit Arguments extensionality.
We also assert propositional extensionality.
Proof irrelevance
Lemma proof_irr: ClassicalFacts.proof_irrelevance.
Proof.
exact (ClassicalFacts.ext_prop_dep_proof_irrel_cic prop_ext).
Qed.
Implicit Arguments proof_irr.