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 Th23:
    q c= (canHom q)"M1
    proof
      reconsider m =(canHom q)"M1 as Ideal of A by Th22;
      for x be object st x in q holds x in (canHom q)"M1
      proof
        let x be object;
        assume
A1:     x in q; then
        x in the carrier of A; then
A3:     x in dom (canHom q) by FUNCT_2:def 1;
        x in ker(canHom q) by A1,RING_2:13; then
        x in {v where v is Element of A : (canHom q).v = 0.(A/q)}
          by VECTSP10:def 9; then
        consider x1 be Element of A such that
A4:     x= x1 and
A5:     (canHom q).x1 = 0.(A/q);
        (canHom q).x in M1 by A5,A4, IDEAL_1:2;
        hence thesis by A3, FUNCT_1:def 7;
      end;
      hence thesis;
    end;
