Известная в узких кругах take lemma для конечных списков через обобщенный take_take:
Lemma take_take_min {T} i j (s : seq T) : take i (take j s) = take (minn i j) s. Proof. by elim: s i j => //= a l IH [|i] [|j] //=; rewrite minnSS IH. Qed.
Lemma take_lemma {T} (p r : seq T) : (forall i, take i p = take i r) <-> p = r. Proof. split; last by move=>->. move=>H; move: (H (size p)) (H (size r)); rewrite !take_size=>{H} Hp Hr. by rewrite Hp -Hr {2 3}Hp !take_take_min minnAC minnn minnC. Qed.
Известная в узких кругах take lemma для конечных списков через обобщенный take_take:
Lemma take_take_min {T} i j (s : seq T) : take i (take j s) = take (minn i j) s. Proof. by elim: s i j => //= a l IH [|i] [|j] //=; rewrite minnSS IH. Qed.
Lemma take_lemma {T} (p r : seq T) : (forall i, take i p = take i r) <-> p = r. Proof. split; last by move=>->. move=>H; move: (H (size p)) (H (size r)); rewrite !take_size=>{H} Hp Hr. by rewrite Hp -Hr {2 3}Hp !take_take_min minnAC minnn minnC. Qed.
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