reserve i,j,m,n,k for Nat,
  x,y for set,
  K for Field,
  a,a1,a2 for Element of K,
  D for non empty set,
  d,d1,d2 for Element of D,
  M,M1,M2 for (Matrix of D),
  A,A1,A2,B1,B2 for (Matrix of K),
  f,g for FinSequence of NAT;
reserve F,F1,F2 for FinSequence_of_Matrix of D,
  G,G9,G1,G2 for FinSequence_of_Matrix of K;
reserve S,S1,S2 for FinSequence_of_Square-Matrix of D,
  R,R1,R2 for FinSequence_of_Square-Matrix of K;
reserve N for (Matrix of n,K),
  N1 for (Matrix of m,K);
reserve p,p1 for FinSequence of K;

theorem Th63:
  mlt(p,<*A*>)=<*p/.1*A*>
proof
A1: dom mlt(p,<*A*>) = dom <*A*> by Def9
    .= Seg 1 by FINSEQ_1:38;
  then 1 in dom mlt(p,<*A*>);
  then
A2: mlt(p,<*A*>).1 = p/.1*(<*A*>.1) by Def9
    .= p/.1*A;
  len mlt(p,<*A*>)=1 by A1,FINSEQ_1:def 3;
  hence thesis by A2,FINSEQ_1:40;
end;
