theorem
  rng f c= dom p implies (p/*f)*g = p/*(f*g)
proof
A1: rng(f*g) c= rng f by RELAT_1:26;
  assume
A2: rng f c= dom p;
  hence (p/*f)*g = p*f*g by Def11
    .= p*(f*g) by RELAT_1:36
    .= p /* (f*g) by A2,A1,Def11,XBOOLE_1:1;
end;
