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) = M2 - M1
proof
  let K be Ring,M1,M2 be Matrix of K;
A1: len (-M1)=len M1 & width (-M1)=width M1 by MATRIX_3:def 2;
  assume
A2: len M1=len M2 & width M1=width M2;
  then len (-M2)=len M1 & width (-M2)=width M1 by MATRIX_3:def 2;
  then -(M1-M2)=-M1+--M2 by Th12
    .=-M1+M2 by Th1
    .=M2+-M1 by A2,A1,MATRIX_3:2;
  hence thesis;
end;
