[codex] Add finset supremum and infimum convergence lemmas#8
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…ommunity#39520) Given `Algebra R S` and an extension `P : Extension R S`, this PR adds `extendScalars` (viewing `P` as an extension of `S` over `P.Ring`), `defaultHom` (the canonical extension homomorphism from the universal extension `R[S] → S` to `P`) and some related linear equivalences on cotangent spaces or the first homology of the naive cotangent complexes. We show the commutativity of the following diagram: <img width="770" height="311" alt="交换图latex" src="https://github.com/user-attachments/assets/e6ad4031-f9ca-4df9-bde3-242ce068bbc1" /> Co-authored-by: @chrisflav
…ar ordered rings (leanprover-community#40565) Mainly, this provides the characterization: `a ≤ b ↔ ℜ a ≤ ℜ b ∧ ℑ a = ℑ b`, but also several related lemmas of convenience.
…of `CostructuredArrow` (leanprover-community#40559) From Proetale and subsequently cleaned up by Claude Fable 5.
…prover-community#40566) We also add a convenience lemma. This is almost trivial from the definition, but it's useful to have the `closedBall` version.
…ompleteLinearOrder` for a finite set without `⊤` (leanprover-community#38356) and more generally, `sSup s ≠ a` for a finite set `s` without `a`, when `a ≠ ⊥`. Also adds the equivalent `sInf`/`iSup`/`iInf` lemmas.
…#38785) Using the `alias_in` attribute for classical CW complexes to get rid of the `export` sections.
) This PR adds the concept of a Bayes estimator for an estimation problem: an estimator that attains the Bayes risk. We can get such estimators by taking an argmin of an integral involving a posterior kernel, when a measurable version of that argmin exists. Co-authored-by: Lorenzo Luccioli @LorenzoLuccioli Co-authored-by: Remy Degenne <remydegenne@gmail.com>
… trimmed measure (leanprover-community#39819) This PR was automatically created from PR leanprover-community#35349 by @RemyDegenne via a [review comment](leanprover-community#35349 (comment)) by @RemyDegenne. Co-authored-by: RemyDegenne <4094732+RemyDegenne@users.noreply.github.com>
Replaces `(by rfl)` with `rfl` whenever possible. Co-authored-by: Batixx <s59fpern@uni-bonn.de>
…40492) Among other things, this removes the coercion from the morphism class into the morphism type, and renames the underlying convenience constructor to `PositiveLinearMap.ofClass`.
…anprover-community#39690) We add new upper bounds on Real.exp in terms of 2x/(2+x), and use these to move some bounds on log higher in mathlib. We also add a lemma for the common bound (1+1/n)^n <= e, though this is a special-case of `one_sub_div_pow_le_exp_neg` (immediately before), but is added for convenience and discoverability, as this is a "well-known" bound.
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Summary
Adds finset-indexed monotone convergence lemmas for suprema and infima:
tendsto_finset_sup_iSupfor complete lattices.tendsto_finset_sup_ciSupfor conditionally complete lattices withOrderBot, assuming a nonempty index type and bounded-above range.tendsto_finset_inf_iInffor complete lattices.tendsto_finset_inf_ciInffor conditionally complete lattices withOrderTop, assuming a nonempty index type and bounded-below range.The conditional versions use the existing
tendsto_atTop_ciSupandtendsto_atTop_ciInftheorems after showing that the indexed supremum/infimum over finite folds agrees with the bounded supremum/infimum of the original family.Validation
lake env lean Mathlib/Topology/Order/MonotoneConvergence.leangit diff --checkEarlier,
lake env scripts/lint-style.py Mathlib/Topology/Order/MonotoneConvergence.leancrashed before checking this file withNameError: name 'nonterminal_simp_check' is not defined.