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New result: List.sorted_range #815

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Merged
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Oct 1, 2025
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New result: List.sorted_range #815

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11 changes: 11 additions & 0 deletions theories/datatypes/List.ec
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Original file line number Diff line number Diff line change
Expand Up @@ -3822,6 +3822,17 @@ rewrite -(perm_cat2l [x]) perm_eq_sym perm_catCl perm_catAC -catA /=.
by rewrite -eqss (@perm_eq_trans s) // perm_sort.
qed.

lemma sorted_range m n : sorted (<) (range m n).
proof.
case: (n <= m); first by move=> ?; rewrite range_geq.
move/ltzNge => lt_mn; rewrite range_ltn //=.
suff: forall m, 0 <= m => forall b n, b < n => path (<) b (range n (n + m)).
- by move=> /(_ (n - (m + 1)) _ m (m+1) _) /#.
move=> {m n lt_mn}; elim=> /= [|m ge0_m ih] b n ?.
- by rewrite range_geq.
by rewrite addrA range_ltn 1:/# /= addrAC; split=> //#.
qed.

(* -------------------------------------------------------------------- *)
(* retrieving a maximal element *)
(* -------------------------------------------------------------------- *)
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