|3: apply (H H3);]
|4: cases H7; clear H7; cases w in H3 H4 H5 H6 H8; simplify; intros;
constructor 1; assumption;]
-qed.
+qed.
definition same_values ≝
λl1,l2:q_f.
∀input.\snd (\fst (value l1 input)) = \snd (\fst (value l2 input)).
definition same_bases ≝
- λl1,l2:q_f.
- (∀i.\fst (nth (bars l1) ▭ i) = \fst (nth (bars l2) ▭ i)).
+ λl1,l2:list bar. (∀i.\fst (nth l1 ▭ i) = \fst (nth l2 ▭ i)).
alias symbol "lt" = "Q less than".
lemma unpos: ∀x:ℚ.OQ < x → ∃r:ratio.Qpos r = x.