Sync upstream mathlib4 (2026-08-05, +12 commits) - #95
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Changes the assumptions of `isCompact_iff_isClosed_bounded` from `[PseudoMetricSpace α] [T2Space α]` to `[MetricSpace α]`, giving the usual metric-space formulation of the Heine–Borel theorem. This requires importing `Mathlib.Topology.MetricSpace.Basic`, which provides `MetricSpace.instT0Space`. Together with the regularity of uniform spaces, this allows `T2Space α` to be inferred from `MetricSpace α`, as needed to show that compact sets are closed. ```lean instance (priority := 100) _root_.MetricSpace.instT0Space : T0Space γ where t0 _ _ h := eq_of_dist_eq_zero <| Metric.inseparable_iff.1 h ```
Specializing existing lemmas for EReal to to real numbers to simplify using them. Found while reviewing #41120 Co-authored-by: Batixx <s59fpern@uni-bonn.de>
…30 (#42433) This PR was automatically created from PR #42430 by @vihdzp via a [review comment](leanprover-community/mathlib4#42430 (comment)) by @grunweg. Co-authored-by: vihdzp <65465670+vihdzp@users.noreply.github.com>
Tags `Hom.ofLE` as `@[implicit_reducible]` to let `rw`/`simp` use `map` API on `mapLe`.
Use `grw`/`gcongr` to golf some proofs. Additionally, deprecate `ENNReal.coe_le_coe_of_le`/`ENNReal.coe_lt_coe_of_lt`, as `gcongr` can now be used on iff lemmas.
…r form version) (#41324) Preliminary lemma for multiplication of a classical distribution by a regular function. The proof is essentially the same as that for `TemperedDistribution`, modulo details.
… #42430 (#42431) This PR was automatically created from PR #42430 by @vihdzp via a [review comment](leanprover-community/mathlib4#42430 (comment)) by @grunweg. Co-authored-by: vihdzp <65465670+vihdzp@users.noreply.github.com>
`Uniform.Completion.extension` maps a map $f:\alpha\to\beta$ to $f:\text{Completion }\alpha \to \beta$. There are theorems that show that this operations preserves continuous, uniformly, continuous and LipschitzWith, but not linearity. This adds that theorem.
This removes an `import all` by switching an `example` that relies on unfolding to a `#guard`. Technically this is testing a different thing—the IR of `mergeSort`, not the expression's unfolding rules—but seeing as this is just an example to demonstrate `mergeSort`, assuming alignment between the compiler and kernel is probably worth the `import all` reduction.
Add `Algebra.denominator` and `Algebra.natDenominator`. For an element `x` of an `R`-algebra `S` with `R` a principal ideal ring, the denominator is a generator of the colon ideal, i.e. of the ideal of scalars `r : R` with `r • x` integral over `R`; over `ℤ`, its absolute value is the natural-number denominator. Part of the Gelfond–Schneider formalization. This PR is self-contained and is itself a prerequisite of the rest of the series. I use Claude code for merging `master` into the branch and for fixing build errors and for moving content around multiple files and for the docstrings. The original formalization was not LLM generated. Co-authored-by: mkaratarakis <mixkarat@gmail.com>
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