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feat(order/filter,topology/instances/nnreal): upgrade some lemmas to iff
#18964
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| @@ -320,6 +320,18 @@ calc a ⊓ x ≤ (b ⊔ y) ⊓ x : inf_le_inf hle le_rfl | |||
| lemma le_sup_right_iff_inf_left_le {a b} (h : is_compl x y) : a ≤ b ⊔ y ↔ a ⊓ x ≤ b := | |||
| ⟨h.inf_left_le_of_le_sup_right, h.symm.dual.inf_left_le_of_le_sup_right⟩ | |||
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| lemma sup_inf_sup_eq (h : is_compl x y) : (a ⊔ x) ⊓ (b ⊔ y) = (b ⊓ x) ⊔ (a ⊓ y) := | |||
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I think sup_inf_sup_comm is the standard name for this type of thing, though usually we'd order it as
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| lemma sup_inf_sup_eq (h : is_compl x y) : (a ⊔ x) ⊓ (b ⊔ y) = (b ⊓ x) ⊔ (a ⊓ y) := | |
| lemma sup_inf_sup_comm (h : is_compl a d) : (a ⊔ b) ⊓ (c ⊔ d) = (a ⊓ c) ⊔ (b ⊓ d) := |
Maybe it's convenient to have both
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codisjoint.inf_left_sup_inf_rightandis_compl.le_inf_sup_inf.filter.comap_ite,filter.comap_max, andfilter.tendsto_ite.real.map_to_nnreal_at_top,real.comap_to_nnreal_at_top, andreal.tendsto_to_nnreal_at_top_iff.tendsto_real_to_nnrealtofilter.tendsto.real_to_nnrealso that it can be used with dot notation.
ennreal.tendsto_of_real_nhds_top.I'm cleaning up old local branches. I don't remember why I wanted to
have these lemmas but IMHO upgrading from implications to
iffs is agood thing.