(* This is how we compute the meet by division by powers of 2 *)

(* Specifications: *)
Lemma nat_meet_mult_power2 q x y : (x*power q 2) ⇣ (y*power q 2)
= (x⇣y)*power q 2.
Lemma nat_meet_euclid_power_2 q r1 d1 r2 d2 :
r1 < power q 2
-> r2 < power q 2
-> (r1+d1*power q 2) ⇣ (r2+d2*power q 2)
= (r1⇣r2) + (d1⇣d2)*power q 2.
Lemma nat_meet_euclid_2 r1 d1 r2 d2 :
r1 < 2
-> r2 < 2
-> (r1+2*d1) ⇣ (r2+2*d2)
= (r1⇣r2) + 2*(d1⇣d2).