whileConvPSemSound : {l : Level} @$\rightarrow$@ (input : Envc) @$\rightarrow$@ ((vari input @$\equiv$@ 0) @$\wedge$@ (varn input @$\equiv$@ c)) implies (varn input + vari input @$\equiv$@ c10 input)
whileConvPSemSound input = proof @$\lambda$@ x @$\rightarrow$@ (conversion input x) where
  conversion : (env : Envc ) @$\rightarrow$@ (vari env @$\equiv$@ 0) @$\wedge$@ (varn env @$\equiv$@ c10 env) @$\rightarrow$@ varn env + vari env @$\equiv$@ c10 env
  conversion e record { pi1 = refl ; pi2 = refl } = +zero