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feat(InfiniteSum): zero function has product zero#39855

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b-mehta:feat/infinitesum-zero-zero
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feat(InfiniteSum): zero function has product zero#39855
b-mehta wants to merge 1 commit into
leanprover-community:masterfrom
b-mehta:feat/infinitesum-zero-zero

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@b-mehta b-mehta commented May 25, 2026

Prove that in a comm monoid with zero, the product of the zero function is zero.


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PR summary 06a5aaf03f

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ hasProd_zero_zero
+ multipliable_zero
+ tprod_zero

You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.


No changes to strong technical debt.
No changes to weak technical debt.

@github-actions github-actions Bot added the t-topology Topological spaces, uniform spaces, metric spaces, filters label May 25, 2026
lemma multipliable_of_exists_eq_zero (hf : ∃ b, f b = 0) [L.LeAtTop] : Multipliable f L :=
⟨0, hasProd_zero_of_exists_eq_zero hf⟩

lemma multipliable_zero [Nonempty β] [L.LeAtTop] : Multipliable (fun _ ↦ 0 : β → α) L :=
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This shouldn't need [Nonempty β] since you can use multipliable_empty

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good point!

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