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feat(library/data/set/basic): add a couple of theorems

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Jeremy Avigad 2016-02-15 22:13:34 -05:00 committed by Leonardo de Moura
parent 03cd2c0013
commit b8d3f34d14
1 changed files with 6 additions and 0 deletions
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library/data/set/basic.lean
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@ -286,6 +286,12 @@ theorem inter_subset_left (s t : set X) : s ∩ t ⊆ s := λ x H, and.left H
theorem inter_subset_right (s t : set X) : s ∩ t ⊆ t := λ x H, and.right H
theorem inter_subset_inter_right {s t : set X} (u : set X) (H : s ⊆ t) : s ∩ u ⊆ t ∩ u :=
take x, assume xsu, and.intro (H (and.left xsu)) (and.right xsu)
theorem inter_subset_inter_left {s t : set X} (u : set X) (H : s ⊆ t) : u ∩ s ⊆ u ∩ t :=
take x, assume xus, and.intro (and.left xus) (H (and.right xus))
theorem subset_inter {s t r : set X} (rs : r ⊆ s) (rt : r ⊆ t) : r ⊆ s ∩ t :=
λ x xr, and.intro (rs xr) (rt xr)