reserve i,j,n,n1,n2,m,k,u for Nat,
        r,r1,r2 for Real,
        x,y for Integer,
        a,b for non trivial Nat;

theorem Th6:
  Px(a,0) = 1 & Py(a,0) = 0
proof
  set A = a^2-'1,M=min_Pell's_solution_of A;
  Px(a,0) + Py(a,0)*sqrt (a^2-'1) = ( M`1 + M`2 *sqrt A ) |^ 0 by Def2
    .= 1+0*sqrt A by NEWTON:4;
  hence thesis by PELLS_EQ:3;
end;
