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 Th18:
  a = i mod p & b = j mod p implies a*b = (i*j) mod p
  proof
    assume a = i mod p & b = j mod p; then
    a*b = ((i mod p) * (j mod p)) mod p by INT_3:def 10;
    hence thesis by NAT_D:67;
  end;
