
theorem Th16:
  for R being Skew-Field, a, b being Element of R, c, d being
  Element of MultGroup R st a = c & b = d holds c*d = a*b
proof
  let R be Skew-Field, a, b be Element of R, c,d be Element of MultGroup R
  such that
A1: a = c & b = d;
  set cMGR = the carrier of MultGroup R;
A2: [c,d] in [:cMGR,cMGR:] by ZFMISC_1:def 2;
  thus c*d = ((the multF of R)||cMGR).(c,d) by Def1
    .= a*b by A1,A2,FUNCT_1:49;
end;
