% arithmetic: 8 points
val times : nat -> nat -> nat
proof timesN00 : !n:nat. (times n 0 = 0)
term timesN00 : !n:nat. (times n 0 = 0)

% symmetry: 12 points
proof symmEq0 : !n:nat. (0 = n => n = 0)
proof symmEqS : !m:nat. (!x:nat. m = x => x = m)
                     => !n:nat. (s m = n => n = s m)
proof symmEq : !m:nat. !n:nat. (m = n => n = m)