reserve n for Nat,
        i,j,i1,i2,i3,i4,i5,i6 for Element of n,
        p,q,r for n-element XFinSequence of NAT;
reserve i,j,n,n1,n2,m,k,l,u,e,p,t for Nat,
        a,b for non trivial Nat,
        x,y for Integer,
        r,q for Real;

theorem Th18:
  Px(a,|.4*x+y.|), Px(a,|.y.|) are_congruent_mod Px(a,|.x.|)
proof
A1: Px(a,|.2*x+y.|) * (-1),(- Px(a,|.y.|))*(-1)
  are_congruent_mod Px(a,|.x.|) by Th17,INT_4:11;
  Px(a,|.2*x+(2*x+y).|),- Px(a,|.2*x+y.|)
  are_congruent_mod Px(a,|.x.|) by Th17;
  hence thesis by A1,INT_1:15;
end;
