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
  t is even & not 4 divides t implies ex u st u = t/2 & u is odd
  proof
    assume
    A1: t is even & not 4 divides t; then
    consider u such that
    A2: t = 2*u by ABIAN:11;
    not 2*2 divides 2*u by A1,A2; then
    u = t/2 & u is odd by A2,LmGCD;
    hence thesis;
  end;
