reserve x,y for Element of REAL;
reserve i,j,k for Element of NAT;
reserve a,b for Element of REAL;

theorem
  for x,y st y <> 0 holds *(*(x,y),inv y) = x
proof
  reconsider jj = 1 as Element of REAL by NUMBERS:19;

  let x,y such that
A1: y <> 0;
  thus *(*(x,y),inv y) = *(x,*(y,inv y)) by Th13
    .= *(x,jj) by A1,Def4
    .= x by Th19;
end;
