Library Coq.Logic.Eqdep

This file axiomatizes the invariance by substitution of reflexive equality proofs [Streicher93] and exports its consequences, such as the injectivity of the projection of the dependent pair.
[Streicher93] T. Streicher, Semantical Investigations into Intensional Type Theory, Habilitationsschrift, LMU M√ľnchen, 1993.

Require Export EqdepFacts.

Module Eq_rect_eq.

Axiom eq_rect_eq :
  forall (U:Type) (p:U) (Q:U -> Type) (x:Q p) (h:p = p), x = eq_rect p Q x p h.

End Eq_rect_eq.

Module EqdepTheory := EqdepTheory(Eq_rect_eq).
Export EqdepTheory.

Exported hints

Hint Resolve eq_dep_eq: eqdep.
Hint Resolve inj_pair2 inj_pairT2: eqdep.