whileLoopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc )
    @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ whileTestStateP s2 env
    @$\rightarrow$@ (next : (env : Envc ) @$\rightarrow$@ (pred n @$\equiv$@ varn env) @$\rightarrow$@ whileTestStateP s2 env  @$\rightarrow$@ t)
    @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ whileTestStateP sf env  @$\rightarrow$@ t) @$\rightarrow$@ t
whileLoopPwP' zero env refl refl _ exit = exit env refl
whileLoopPwP' (suc n) env refl refl next _ =
    next (record env {varn = pred (varn env) ; vari = suc (vari env) }) refl (+-suc n (vari env))


loopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc )
    @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ whileTestStateP s2 env
    @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ whileTestStateP sf env @$\rightarrow$@ t) @$\rightarrow$@ t
loopPwP' zero env refl refl exit = exit env refl
loopPwP' (suc n) env refl refl exit
    = whileLoopPwP' (suc n) env refl refl (@$\lambda$@ env x y @$\rightarrow$@ loopPwP' n env x y exit) exit