Peter LeFanu Lumsdaine peterlefanulumsdaine
peterlefanulumsdaine
/ Term that cannot be given explicitly
Last active
December 14, 2015 00:38
Code attachment for [this issue](https://github.com/HoTT/coq/issues/19) on [HoTT/coq](https://github.com/HoTT/coq)
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| Inductive equals {A : Type} (a : A) : A -> Type := | |
| refl : equals a a. | |
| Arguments refl {A a} , [A] a. | |
| Notation "x = y" := (equals x y). | |
| Definition flip {A B : Type} {P : A -> B -> Type} | |
| : (forall a b, P a b) -> (forall b a, P a b) | |
| := fun f b a => f a b. |
peterlefanulumsdaine
/ why_not_omega.v
Created
June 25, 2011 04:37
Somewhere that omega doesn’t work, where I’d expect it would.
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| Lemma list_filterremove_less x l: (InA E.eq x l) -> length (List.filter (fun y => if E.eq_dec y x then false else true) l) < length l. | |
| Proof. | |
| intros H_xinl. induction H_xinl as [ y l' H_xy | y l' H_xl' IHH]. | |
| Case "x = y, l = y :: l'". | |
| simpl. destruct (F.eq_dec y x) as [H_yes | H_no]. | |
| SCase "F.eq_dec y x = yes". | |
| assert (length (List.filter (fun y0 : E.t => if F.eq_dec y0 x then false else true) l') <= length l') by (apply filter_length). unfold lt. | |
| (* omega. *) | |
| apply Le.le_n_S; assumption. (* Why doesn’t [omega] work? *) |