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feat(topology/algebra/infinite_sum): Extract none from a sum over option types - #19150
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dtumad wants to merge 2 commits into
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feat(topology/algebra/infinite_sum): Extract none from a sum over option types#19150dtumad wants to merge 2 commits into
none from a sum over option types#19150dtumad wants to merge 2 commits into
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dtumad
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Jun 4, 2023
eric-wieser
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none from a some over option typesnone from a sum over option types
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| exact if_neg hb' | ||
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| lemma has_sum_singleton (f : β → α) (b : β) : has_sum (f ∘ coe : ({b} : set β) → α) (f b) := |
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Please add it for a [unique] type, not just a singleton.
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| has_sum f (a + b) := | ||
| ha.add_is_compl is_compl_compl.symm hb | ||
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| lemma has_sum.sum_t {f : β ⊕ γ → α} {a_inl a_inr : α} (h_inl : has_sum (f ∘ sum.inl) a_inl) |
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There are two ways to state this lemma: starting with β ⊕ γ → α and starting with two functions and combining them using sum.elim. Please add the second version too (the proof should be by application of this version). I'm not sure about the naming convention for this kind of lemmas. sum_dom? I would ask on Zulip.
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| has_sum.add_is_compl (set.is_compl_range_inl_range_inr) | ||
| (sum.inl_injective.has_sum_range_iff.2 h_inl) (sum.inr_injective.has_sum_range_iff.2 h_inr) | ||
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| lemma has_sum.option {f : option β → α} {a_some : α} (hf : has_sum (f ∘ option.some) a_some) : |
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Also, please add summable versions of your lemmas (with iff versions whenever we can apply summable.comp_injective).
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This PR gives lemmas for separating a sum over
option αinto the value atnoneplus a sum overα