theorem Th46:
  Len S = Width S
proof
  set L=Len S;
  set W=Width S;
A1: dom W=dom S by Def4;
A2: dom L=dom S by Def3;
  now
    let k such that
A3: k in dom L;
    thus L.k = len (S.k) by A3,Def3
      .= width (S.k) by MATRIX_0:24
      .= W.k by A2,A1,A3,Def4;
  end;
  hence thesis by A2,A1,FINSEQ_1:13;
end;
