reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  for a,b be positive Nat holds a mod b = b mod a implies a = b
  proof
    let a,b be positive Nat;
    per cases by XXREAL_0:1;
    suppose
      a < b; then
      a mod b = a by NAT_D:24;
      hence thesis by NAT_D:1;
    end;
    suppose
      b < a; then
      b mod a = b by NAT_D:24;
      hence thesis by NAT_D:1;
    end;
    suppose b = a;
      hence thesis;
    end;
  end;
