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

-- Hoare Logic base CodeGear
whileLoopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc )
  @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ (pre : varn env + vari env @$\equiv$@ c10 env)
  @$\rightarrow$@ (next : (env : Envc ) @$\rightarrow$@ (pred n @$\equiv$@ varn env) @$\rightarrow$@ (post : varn env + vari env @$\equiv$@ c10 env) @$\rightarrow$@ t)
  @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ (fin : vari env @$\equiv$@ c10 env)  @$\rightarrow$@ t) @$\rightarrow$@ t
whileLoopPwP' zero env refl refl next exit = exit env refl
whileLoopPwP' (suc n) env refl refl next exit = next (record env {varn = pred (varn env) ; vari = suc (vari env) }) refl (+-suc n (vari env))