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Added lemmas proving consequences of a list concatenation being []. #924

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strub merged 1 commit into from
Mar 9, 2026
Merged

Added lemmas proving consequences of a list concatenation being []. #924

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9 changes: 9 additions & 0 deletions theories/datatypes/List.ec
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Expand Up @@ -184,6 +184,15 @@ proof. by elim: s1 x => [|y s1 ih] x //=; rewrite ih. qed.
lemma belast_rcons x s z : belast<:'a> x (rcons s z) = x :: s.
proof. by rewrite lastI -!cats1 belast_cat. qed.

lemma cat_eq0I (xs ys : 'a list) : xs ++ ys = [] => xs = [] /\ ys = [].
proof. by case: xs. qed.

lemma cat_eq0IL (xs ys : 'a list) : xs ++ ys = [] => xs = [].
proof. by case: xs. qed.

lemma cat_eq0IR (xs ys : 'a list) : xs ++ ys = [] => ys = [].
proof. by case: xs. qed.

(* -------------------------------------------------------------------- *)
(* rcons / induction principle *)
(* -------------------------------------------------------------------- *)
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