reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve K,K1,K2,K3 for Field;
reserve SK1,SK2 for Subfield of K;
reserve ek,ek1,ek2 for Element of K;
reserve p for Prime;
reserve a,b,c for Element of GF(p);
reserve F for FinSequence of GF(p);

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;
