reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;
reserve p,q for natural Number;
reserve i0,i,i1,i2,i4 for Integer;
reserve x for set;
reserve p for Prime;
reserve i for Nat;

theorem
  for x being Complex holds x |^ 2 = x * x & x^2 = x |^ 2
proof
  let x be Complex;
  thus x * x = (x |^ 1) * x
    .= x |^ (1+1) by Th6
    .= x |^ 2;
  hence thesis;
end;
