reserve R for commutative Ring;
reserve A for non degenerated commutative Ring;
reserve I,J,q for Ideal of A;
reserve p for prime Ideal of A;
reserve M,M1,M2 for Ideal of A/q;

theorem Th27:
    M1 c= M2 implies (canHom q)"M1 c= (canHom q)"M2
    proof
      assume
A1:   M1 c= M2;
      for x be Element of the carrier of A st x in (canHom q)"M1
      holds x in (canHom q)"M2
      proof
        let x be Element of the carrier of A;
        assume x in (canHom q)"M1; then
        x in dom canHom q & (canHom q).x in M1 by FUNCT_1:def 7;
        hence thesis by FUNCT_1:def 7,A1;
      end;
      hence thesis;
    end;
