reserve x,y for set,
  n,m for Nat,
  r,s for Real;

theorem
  for r,s be Real holds MIM(<*r,s*>) = <*r-s,s*>
proof
  let r,s be Real;
   reconsider r,s as Element of REAL by XREAL_0:def 1;
  set f = <*r,s*>;
A1: len f = 2 & f.1 = r by FINSEQ_1:44;
A2: f.2 = s;
  0 qua Nat+2 = 2 & 0 qua Nat +1 = 1;
  then MIM(f) = MIM(f)|0 ^ <*r-s,s*> by A1,A2,Th11;
  hence thesis by FINSEQ_1:34;
end;
