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solve_ndisj.v 995 B
From stdpp Require Import namespaces strings.
Section tests.
Implicit Types (N : namespace) (E : coPset).
Lemma test1 N1 N2 :
N1 ## N2 → ↑N1 ⊆@{coPset} ⊤ ∖ ↑N2.
Proof. solve_ndisj. Qed.
Lemma test2 N1 N2 :
N1 ## N2 → ↑N1.@"x" ⊆@{coPset} ⊤ ∖ ↑N1.@"y" ∖ ↑N2.
Proof. solve_ndisj. Qed.
Lemma test3 N :
⊤ ∖ ↑N ⊆@{coPset} ⊤ ∖ ↑N.@"x".
Proof. solve_ndisj. Qed.
Lemma test4 N :
⊤ ∖ ↑N ⊆@{coPset} ⊤ ∖ ↑N.@"x" ∖ ↑N.@"y".
Proof. solve_ndisj. Qed.
Lemma test5 N1 N2 :
⊤ ∖ ↑N1 ∖ ↑N2 ⊆@{coPset} ⊤ ∖ ↑N1.@"x" ∖ ↑N2 ∖ ↑N1.@"y".
Proof. solve_ndisj. Qed.
Lemma test_ndisjoint_difference_l N : ⊤ ∖ ↑N ##@{coPset} ↑N.
Proof. solve_ndisj. Qed.
Lemma test_ndisjoint_difference_r N : ↑N ##@{coPset} ⊤ ∖ ↑N.
Proof. solve_ndisj. Qed.
Lemma test6 E N :
↑N ⊆ E → ↑N ⊆ ⊤ ∖ (E ∖ ↑N).
Proof. solve_ndisj. Qed.
Lemma test7 N :
↑N ⊆@{coPset} ⊤ ∖ ∅.
Proof. solve_ndisj. Qed.