@@ -697,6 +697,22 @@ maximumSuccSucc (S left) (S right) =
697 let inductiveHypothesis = maximumSuccSucc left right in
697 let inductiveHypothesis = maximumSuccSucc left right in
698 ?maximumSuccSuccStepCase
698 ?maximumSuccSuccStepCase
700+total sucMaxL : (l : Nat) -> maximum (S l) l = (S l)
702+sucMaxL (S l) = cong (sucMaxL l)
704+total sucMaxR : (l : Nat) -> maximum l (S l) = (S l)
706+sucMaxR (S l) = cong (sucMaxR l)
708+total sucMinL : (l : Nat) -> minimum (S l) l = l
710+sucMinL (S l) = cong (sucMinL l)
712+total sucMinR : (l : Nat) -> minimum l (S l) = l
714+sucMinR (S l) = cong (sucMinR l)
700-- div and mod
716-- div and mod
701total modZeroZero : (n : Nat) -> mod 0 n = Z
717total modZeroZero : (n : Nat) -> mod 0 n = Z
702modZeroZero Z = refl
718modZeroZero Z = refl