
theorem Th16:
for M be Matrix of ExtREAL holds
   len Sum M = len M
 & for i be Nat st i in Seg len M holds (Sum M).i=Sum Line(M,i)
proof
  let M be Matrix of ExtREAL;
  thus len Sum M = len M by Def5;
  thus for k be Nat st k in Seg len M holds (Sum M).k=Sum Line(M,k)
  proof
    let k be Nat such that
A1: k in Seg len M;
A2: k in dom M by A1,FINSEQ_1:def 3;
    k in Seg len Sum M by A1,Def5;
    then k in dom Sum M by FINSEQ_1:def 3;
    hence (Sum M).k = Sum(M.k) by Def5
      .= Sum(Line(M,k)) by A2,MATRIX_0:60;
  end;
end;
