33 lines
763 B
Coq
33 lines
763 B
Coq
Require Import subsequences.
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Require Import Sorting.Permutation.
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Require Import Nat.
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Require Import PeanoNat.
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Require Import List.
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Import ListNotations.
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Definition complete_sequence {X: Type} (u base : list X) :=
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forall v, Permutation base v -> subsequence u v.
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Definition shortest_complete_sequence {X: Type} (u base : list X) :=
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complete_sequence u base
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/\ forall v, length v < length u -> ~ complete_sequence v base.
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Theorem complete_sequence_rev {X: Type} :
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forall (u base : list X),
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complete_sequence u base -> complete_sequence (rev u) base.
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Proof.
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intros u base. intro H.
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intro p. intro I. apply subsequence_rev. rewrite rev_involutive.
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apply H. apply Permutation_trans with (l' := p). assumption.
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apply Permutation_rev.
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Qed.
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