Coq: Stuck using the subtype

Question

I have following definitions: (definition of positive integers as a subtype of nat)

Definition Z_pos_filter (p: nat) : bool :=
  if (beq_nat p 0) then false else         


        

Answer 1

IMHO answering this question in the original form is advocating a questionable style. I think that multiplication for such numbers should be just the multiplication of the base type; and the proof should just follow from injectivity of the projection, as is done in mathcomp.

In general, you are going to have quite a lot of problems if non-fully opaque proofs appear in your terms after reduction.