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Add set of lemmas for esum - #2062

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lyonel2017:feature-esum-lemmas
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Add set of lemmas for esum#2062
lyonel2017 wants to merge 2 commits into
math-comp:masterfrom
lyonel2017:feature-esum-lemmas

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@lyonel2017

@lyonel2017 lyonel2017 commented Jul 29, 2026

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Motivation for this change

Set of lemmas for esum extracted from #2049.

Checklist
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers
Reminder to reviewers

This was referenced Jul 29, 2026
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@affeldt-aist affeldt-aist added this to the 1.18.0 milestone Jul 30, 2026
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Sorry for the random, minor comments.
Yet, I am already concerned by the fact that we have summable defined both in esum.v and in realsum.v: we might want to distinguish one or the other by adding a small e or a small r in the identifier.

@affeldt-aist affeldt-aist added the enhancement ✨ This issue/PR is about adding new features enhancing the library label Jul 30, 2026
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I made a first pass. I have not yet looked at section esum_summable.
I'll complete this review asap.

Maybe we do not need pos_neq0_esum
(btw, let's keep the substring pos_esum in identifiers
so that we remember easily that we are inside the PosEsum module)
since it is not used and in fact the more general
version neq0_esum (rather: esum_neq0) does not require
non-negativity as an hypothesis
(so far, the rationale was to use the PosEsum module to hold
restricted versions of esum lemmas for non-negative functions).

pos_sum_esum_ge: we can suppress because this is really
just a special case of pos_esum_ge and is used only once.

summable_muleC is maybe not necessary since it is really
just under eq_fun do rewrite muleC

Pending:
pos_esum_ge1/esum_ge1: there might be a better name
(_ge1 looks too much like 1 <= _) but I have not idea yet

esum_unit does not mention unit, maybe esum_if_eq_op_set1
but the script is so short that maybe the lemma is not really useful

TODO: the changelog should mention that le_esum has been generalized

fyi: @strub

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