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 Th16:
  a = i mod p implies -a = (p-i) mod p
  proof
    assume A1: a = i mod p;
    reconsider b = (p-i) mod p as Element of GF(p) by Th14;
    a+b = (i+(p-i)) mod p by A1,Th15
    .= 0 by INT_1:50
    .= 0.GF(p) by Th11;
    hence thesis by VECTSP_1:16;
  end;
