reserve x,y,z for Real,
  x3,y3 for Real,
  p for Point of TOP-REAL 3;
reserve p1,p2,p3,p4 for Point of TOP-REAL 3,
  x1,x2,y1,y2,z1,z2 for Real;

theorem Th28:
  for f1, f2 be FinSequence of REAL st len f1 = 3 & len f2 = 3
  holds mlt(f1, f2) = <* f1.1*f2.1, f1.2*f2.2, f1.3*f2.3 *>
proof
  let f1, f2 be FinSequence of REAL such that
A1: len f1 = 3 and
A2: len f2 = 3;
A3: f2 = <* f2.1, f2.2, f2.3 *> by A2,FINSEQ_1:45;
  reconsider f11=f1.1, f12=f1.2, f13=f1.3, f21=f2.1, f22=f2.2, f23=f2.3
    as Element of REAL by XREAL_0:def 1;
  mlt(f1, f2) = multreal.:(f1, f2) by RVSUM_1:def 9
    .= multreal.:(<* f11, f12, f13 *>, <* f21, f22, f23 *>)
      by A1,A3,FINSEQ_1:45
    .= <* multreal.(f1.1, f2.1), multreal.(f1.2, f2.2), multreal.(f1.3, f2.3
  )*> by FINSEQ_2:76
    .= <* f1.1*f2.1, multreal.(f1.2, f2.2), multreal.(f1.3, f2.3)*> by
BINOP_2:def 11
    .= <* f1.1*f2.1, f1.2*f2.2, multreal.(f1.3, f2.3)*> by BINOP_2:def 11;
  hence thesis by BINOP_2:def 11;
end;
