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 & M1 + -M2 = 0.(K,len M1,width M1) holds M1 = M2
proof
  let K be Ring,M1,M2 be Matrix of K;
  assume that
A1: len M1=len M2 & width M1=width M2 and
A2: M1 + -M2 = 0.(K,len M1,width M1);
  M1-M2=0.(K,len M1,width M1) by A2;
  hence thesis by A1,Th7;
end;
