whileTestPCallwP!$\prime$! : (c :  !$\mathbb{N}$! ) !$\rightarrow$! Set
whileTestPCallwP!$\prime$! c = whileTestPwP {_} {_} c (!$\lambda$! env s !$\rightarrow$! loopPwP!$\prime$! (varn env) env refl (conv env s) ( !$\lambda$! env s !$\rightarrow$! vari env !$\equiv$! c10 env )  )


-- conv : (env : Envc ) !$\rightarrow$! (vari env !$\equiv$! 0) !$\wedge$! (varn env !$\equiv$! c10 env) !$\rightarrow$! varn env + vari env !$\equiv$! c10 env
-- conv e record { pi1 = refl ; pi2 = refl } = +zero