For each of the following statements, point out which ones are definitions and which ones \ are the orems for x; y2N. Prove the theorems using only definitions and statements proven above. a) x =...

For each of the following statements, point out which ones are definitions and which ones \

are the orems for x; y2N. Prove the theorems using only definitions and statements proven

above.

a) x = x + 0,

b) x = 0 + x,

c) x+ (y+1) = (x+y) + 1,

d) (x+1) + y = (y+x) + 1,

e) x 0 = 0,

f) 0 x = 0,

g) 5 + 1 = 6,

h) 7 + 4 = 11.

Prove Lemma 5.

Prove the following properties of exponentiation for

a; b; c 2 N.