reserve i,j for Nat;

theorem
  for K being Ring,M1,M2 being Matrix of K st len M1=len M2 & width M1=
  width M2 holds M1=(-M2+M1)+M2
proof
  let K be Ring,M1,M2 be Matrix of K;
  assume
A1: len M1=len M2 & width M1=width M2;
  then len (-M2)=len M1 & width (-M2)=width M1 by MATRIX_3:def 2;
  then (-M2+M1)+M2=M1-M2+M2 by MATRIX_3:2;
  hence thesis by A1,Th22;
end;
