reserve X,Y for set;
reserve R for domRing-like commutative Ring;
reserve c for Element of R;

theorem Th8:
  for a,b being Element of R holds
  b divides a & b <> 0.R implies (a/b = 0.R iff a = 0.R)
proof
  let a,b be Element of R;
  assume that
A1: b divides a and
A2: b <> 0.R;
  hereby
    assume a/b = 0.R;
    then a = 0.R * b by A1,A2,Def4
      .= 0.R;
    hence a = 0.R;
  end;
  assume a = 0.R;
  then 0.R = (a/b) * b by A1,A2,Def4;
  hence thesis by A2,VECTSP_2:def 1;
end;
