whileTestPSemSound : (c : @$\mathbb{N}$@ ) (output : Envc )
  @$\rightarrow$@ output @$\equiv$@ whileTestP c (@$\lambda$@ e @$\rightarrow$@ e)
  @$\rightarrow$@ @$\top$@ implies ((vari output @$\equiv$@ 0) @$\wedge$@ (varn output @$\equiv$@ c))
  whileTestPSemSound c output refl = proof (@$\lambda$@ _ @$\rightarrow$@ record { pi1 = refl ; pi2 = refl })