theorem Th15:
  a = i mod p & b = j mod p implies a+b = (i+j) mod p
  proof
    assume A1: a = i mod p & b = j mod p;
    a+b = ((i mod p) + (j mod p)) mod p by A1,GR_CY_1:def 4;
    hence thesis by NAT_D:66;
  end;
