theorem
  \Cap(M,A) \iff A\and(M*A)\and\Cap(M, (M\;M)*A) in H
  proof
A1: \Cap(M,A) \iff A\and\Cap(M, M*A) in H by Def43;
    \Cap(M,M*A) \iff (M*A)\and\Cap(M, M*(M*A)) in H by Def43;
    then
A2: \Cap(M,A) \iff A\and((M*A)\and\Cap(M, M*(M*A))) in H by A1,Th97;
    A\and(M*A)\and\Cap(M, M*(M*A))\iffA\and((M*A)\and\Cap(M, M*(M*A))) in H
    by Th78;
    then A\and((M*A)\and\Cap(M, M*(M*A)))\iffA\and(M*A)\and\Cap(M, M*(M*A))
    in H by Th90;
    then
A3: \Cap(M,A) \iff A\and(M*A)\and\Cap(M, M*(M*A)) in H by A2,Th91;
    ((M\;M)*A)\iff(M*(M*A)) in H by Def43;
    then (M*(M*A)) \iff ((M\;M)*A) in H by Th90;
    then \Cap(M, M*(M*A))\iff\Cap(M, (M\;M)*A) in H by Th148;
    hence thesis by A3,Th97;
  end;
