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 len M1=len M2 & width M1=width M2;
  then
A1: len (-M2)=len M1 & width (-M2)=width M1 by MATRIX_3:def 2;
  len (-M1)=len M1 & width (-M1)=width M1 by MATRIX_3:def 2;
  then -(-M1+-M2)=--M1+--M2 by A1,Th12
    .=M1+--M2 by Th1;
  hence thesis by Th1;
end;
