reserve i,j for Nat;

theorem Th22:
  for K being Ring,M1,M2 being Matrix of K st len M1=len M2 &
  width M1=width M2 holds M1 = M1 - M2 + M2
proof
  let K be Ring,M1,M2 be Matrix of K;
  assume
A1: len M1=len M2 & width M1=width M2;
  then
A2: len (-M2)=len M1 & width (-M2)=width M1 by MATRIX_3:def 2;
  hence M1 - M2 + M2=M1+(-M2+M2) by MATRIX_3:3
    .=M1+(M2-M2) by A1,A2,MATRIX_3:2
    .=M1 by A1,Th20;
end;
