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 München, 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: core v62.

Hint Resolve inj_pair2 inj_pairT2: core.