theorem
  M*\notV in H & A in H or M*V in H & M*(M1*(while(M,M1)*A)) in H implies
  while(M,M1)*A in H
  proof
    assume M*\notV in H & A in H or M*V in H & M*(M1*(while(M,M1)*A)) in H;
    then
A1: (M*\notV)\andA in H or (M*V)\and(M*(M1*(while(M,M1)*A))) in H
    by Th35;
    ((M*\notV)\andA)\imp((M*\notV)\andA)\or
    ((M*V)\and(M*(M1*(while(M,M1)*A)))) in H &
    ((M*V)\and(M*(M1*(while(M,M1)*A))))\imp((M*\notV)\andA)\or
    ((M*V)\and(M*(M1*(while(M,M1)*A)))) in H by Def38;
    then
A2: ((M*\notV)\andA)\or((M*V)\and(M*(M1*(while(M,M1)*A)))) in H
    by A1,Def38;
    (while(M,M1)*A) \iff
    ((M*\notV)\andA)\or((M*V)\and(M*(M1*(while(M,M1)*A)))) in H by Def43;
    then
    ((M*\notV)\andA)\or((M*V)\and(M*(M1*(while(M,M1)*A))))\imp
    (while(M,M1)*A) in H by Th43;
    hence thesis by Def38,A2;
  end;
