reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem SUD:
  for a,b be Integer, p be odd prime Nat st not p divides b holds
  p divides (a-b) implies not p divides (a+b)
  proof
    let a,b be Integer, p be odd prime Nat such that
    A1: not p divides b;
    p gcd 2 = 1 by Def3; then
    not p divides 2 by INT_2:28, PEPIN:2, PYTHTRIP:def 2; then
    A2: not p divides 2*b by A1,INT_5:7;
    assume p divides (a-b); then
    not p divides ((a-b) + 2*b) by A2,INT_2:1;
    hence thesis;
  end;
