Commit f56f3834 authored by Ralf Jung's avatar Ralf Jung
Browse files

add big_sepS_elem_of_acc_impl

parent 69cd8d4f
...@@ -1782,6 +1782,22 @@ Section gset. ...@@ -1782,6 +1782,22 @@ Section gset.
by setoid_rewrite wand_elim_l. by setoid_rewrite wand_elim_l.
Qed. Qed.
Lemma big_sepS_elem_of_acc_impl x Φ X :
x X
([ set] y X, Φ y) - Φ x
( Ψ, Ψ x - ( y, y X y x Φ y - Ψ y) - ([ set] y X, Ψ y)).
intros Helem. rewrite big_sepS_delete //. apply sep_mono_r.
apply forall_intro=>Ψ.
rewrite (big_sepS_impl Φ Ψ).
rewrite wand_curry comm -wand_curry. apply wand_intro_r.
assert ( a : A, a X a x a X {[x]}) as Hiff by set_solver.
setoid_rewrite Hiff.
rewrite wand_elim_l.
apply wand_intro_l.
rewrite -big_sepS_delete //.
Lemma big_sepS_dup P `{!Affine P} X : Lemma big_sepS_dup P `{!Affine P} X :
(P - P P) - P - [ set] x X, P. (P - P P) - P - [ set] x X, P.
Proof. Proof.
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