proposition: Lemma sqrt2_step_def rec ih il j: sqrt2_step rec ih il j = if (ih <? j)%uint63 then let quo := fst (diveucl_21 ih il j) in if (quo <? j)%uint63 then let m := match j +c quo with | C0 m1 => m1 >> 1 | C1 m1 => (m1 >> 1 + 1 << (digits -1))%uint63 end in rec ih il m else j else j.
proof: Proof. unfold sqrt2_step; case diveucl_21; intros i j';simpl. case (j +c i);trivial. Qed.
imports: Utf8 DoubleType Lia Zpow_facts Zgcd_alt PrimInt63