Commit 8edee98e authored by Robbert Krebbers's avatar Robbert Krebbers

Make `set_seq` lemmas for consistent w.r.t. those of maps.

parent 668baa2b
......@@ -1055,23 +1055,36 @@ Section set_seq.
- rewrite elem_of_union, elem_of_singleton, IH. lia.
Qed.
Lemma set_seq_start_disjoint start len :
Lemma set_seq_plus_disjoint start len1 len2 :
set_seq (C:=C) start len1 ## set_seq (start + len1) len2.
Proof. intros x. rewrite !elem_of_set_seq. lia. Qed.
Lemma set_seq_plus start len1 len2 :
set_seq (C:=C) start (len1 + len2)
set_seq start len1 set_seq (start + len1) len2.
Proof. intros x. rewrite elem_of_union, !elem_of_set_seq. lia. Qed.
Lemma set_seq_plus_L `{!LeibnizEquiv C} start len1 len2 :
set_seq (C:=C) start (len1 + len2)
= set_seq start len1 set_seq (start + len1) len2.
Proof. unfold_leibniz. apply set_seq_plus. Qed.
Lemma set_seq_S_start_disjoint start len :
{[ start ]} ## set_seq (C:=C) (S start) len.
Proof. intros x. rewrite elem_of_singleton, elem_of_set_seq. lia. Qed.
Lemma set_seq_S_start start len :
set_seq (C:=C) start (S len) {[ start ]} set_seq (S start) len.
Proof. done. Qed.
Lemma set_seq_S_disjoint start len :
Lemma set_seq_S_end_disjoint start len :
{[ start + len ]} ## set_seq (C:=C) start len.
Proof. intros x. rewrite elem_of_singleton, elem_of_set_seq. lia. Qed.
Lemma set_seq_S_union start len :
Lemma set_seq_S_end_union start len :
set_seq start (S len) @{C} {[ start + len ]} set_seq start len.
Proof.
intros x. rewrite elem_of_union, elem_of_singleton, !elem_of_set_seq. lia.
Qed.
Lemma set_seq_S_union_L `{!LeibnizEquiv C} start len :
Lemma set_seq_S_end_union_L `{!LeibnizEquiv C} start len :
set_seq start (S len) =@{C} {[ start + len ]} set_seq start len.
Proof. unfold_leibniz. apply set_seq_S_union. Qed.
Proof. unfold_leibniz. apply set_seq_S_end_union. Qed.
End set_seq.
(** Mimimal elements *)
......
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