reserve i,j for Nat;

theorem Th62:
  for x being FinSequence of REAL, A being Matrix of REAL st len A
  =len x holds len (x*A) = width A
proof
  let x be FinSequence of REAL, A be Matrix of REAL;
  assume
A1: len A=len x;
A2: width LineVec2Mx x=len x by Def10;
  len Line((LineVec2Mx x)*A,1)=width (MXF2MXR ((MXR2MXF (LineVec2Mx x))*(
  MXR2MXF A))) by MATRIX_0:def 7
    .=width A by A1,A2,MATRIX_3:def 4;
  hence thesis;
end;
