reserve i,j for Nat;

theorem Th61:
  for x being FinSequence of REAL, A being Matrix of REAL st width
  A=len x & len x>0 holds len (A*x) = len A
proof
  let x be FinSequence of REAL, A be Matrix of REAL;
  assume that
A1: width A=len x and
A2: len x>0;
A3: len ColVec2Mx x=len x by A2,Def9;
  len (Col(A*(ColVec2Mx x),1))=len (A*(ColVec2Mx x)) by MATRIX_0:def 8
    .=len A by A1,A3,MATRIX_3:def 4;
  hence thesis;
end;
