Let m be an even integer. Note that m + 2 is even. Let m be an odd integer. Observe that m + 2 is odd. Let m be a non empty natural number. Observe that 2 is even. Let n be an even natural number and let m be a non empty natural number. Note that n is even. We now state several propositions: (2) If r 6= 0, then 1 r · ri+1 = r. (3) If r s is an integer and s 6= 0, then −⌊ r s ⌋ = ⌊ s ⌋ + 1. (4) ...
