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Thomas Baruchel 2023-10-30 14:11:21 +01:00
parent 9325baf42b
commit 81f0311165
1 changed files with 0 additions and 78 deletions
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78
src/subsequences.v
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@ -183,16 +183,6 @@ Proof.
intro s. assert({subsequence2 l s} + {~ subsequence2 l s}). apply IHl.
destruct H0.
(*
left. destruct s0.
destruct H0. exists (false::x). split. simpl. rewrite H0. reflexivity.
simpl. assumption.
destruct s. left. apply subsequence2_nil_r.
assert ({T=a}+{T<>a}). apply H. destruct H0.
rewrite e.
*)
rewrite <- subsequence2_cons_eq with (a := a) in s0.
apply subsequence2_cons_r in s0. left. assumption.
@ -213,74 +203,6 @@ Proof.
Qed.
(*
Theorem subsequence_dec : forall (l s : list Type),
{ subsequence l s } + { ~ subsequence l s }.
Proof.
intros l s. generalize l. induction s. left. apply subsequence_nil_r.
intro l0. destruct l0. right. apply subsequence_nil_cons_r.
intros l s. induction s. left. apply subsequence_nil_r.
destruct l. right. apply subsequence_nil_cons_r.
unfold subsequence2. destruct s. simpl.
left. exists nil. easy. right.
unfold not. intro H. destruct H. destruct H.
rewrite combine_nil in H0.
symmetry in H0. apply nil_cons in H0. assumption.
destruct IHl. left. unfold subsequence2. assert (H := s0).
unfold subsequence2 in H. destruct H. destruct H.
exists (false::x). split. simpl. apply eq_S. assumption.
assumption.
(* destructurer s puis tester les deux cas : a = (car s) ou non *)
destruct s. left. unfold subsequence2.
Theorem subsequence_dec : forall (l s : list nat),
{ subsequence2 l s } + { ~ subsequence2 l s }.
Proof.
intros l s. induction l.
unfold subsequence2. destruct s. simpl.
left. exists nil. easy. right.
unfold not. intro H. destruct H. destruct H.
rewrite combine_nil in H0.
symmetry in H0. apply nil_cons in H0. assumption.
destruct IHl. left. unfold subsequence2. assert (H := s0).
unfold subsequence2 in H. destruct H. destruct H.
exists (false::x). split. simpl. apply eq_S. assumption.
assumption.
(* destructurer s puis tester les deux cas : a = (car s) ou non *)
destruct s. left. unfold subsequence2.
exists (repeat false (S (length l))). rewrite repeat_length.
split. easy. simpl.
assert (forall u,
(nil: list nat)
= map snd (filter fst (combine (repeat false (length u)) u))).
intro u. induction u. reflexivity. simpl. assumption. apply H.
assert ({a=n0}+{a<>n0}). apply PeanoNat.Nat.eq_dec. destruct H.
*)
Theorem subsequence_eq_def :
(forall x y : Type, {x = y} + {x <> y})
-> (forall l s, subsequence l s <-> subsequence2 l s).