feat(Topology/Algebra/Module/Spaces/ContinuousLinearMap): convert toLinearMap₁₂ to a linear map

[mpacholski]

Convert the projection toLinearMap₁₂ (which strips the topology from a continuous semibilinear map) to a linear map, by showing that it preserves addition and scalar multiplication, and mark it with @[simp apply] absorb the toLinearMap₁₂_apply lemma.

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PR summary 242e4da0dd

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

No declarations were harmed in the making of this PR! 🐙

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.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 242e4da0dd
Reference commit 4a73a604a6

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[pechersky]

Does it make sense to upgrade toLinearMap₁₂ to a linear map of ContinuousLinearMaps instead of having it unbundled?

[mpacholski]

@pechersky thank you for the comment! Can't say that I see a reason to have it unbundled. Shall I convert it to a linear map and update the PR?

[mpacholski]

@pechersky I converted it to a bundled linear map, and also marked it with @[simp apply]. Do you think it's good now?

[pechersky]

What were the new simps lemmas? You can check via simps?.

[mpacholski]

Using simps? shows that the generated lemma is just

@[simp] lemma toLinearMap₁₂_apply (L : E →SL[σ₁₃] F →SL[σ₂₃] G) :
  toLinearMap₁₂ L = coeLMₛₗ σ₂₃ ∘ₛₗ ↑L

Should we use just @[simps] instead of @[simps apply]?

I also checked @[simps!? apply_apply] and it generates

@[simp] lemma toLinearMap₁₂_apply_apply (L : E →SL[σ₁₃] F →SL[σ₂₃] G) (v : E) :
  toLinearMap₁₂ L v = ↑(L v)

[themathqueen]

I don't think apply here will be the same as the one we had before.

[mpacholski]

you're right, as I checked with @[simp?] the generated lemma is

@[simp] lemma toLinearMap₁₂_apply (L : E →SL[σ₁₃] F →SL[σ₂₃] G) :
  toLinearMap₁₂ L = coeLMₛₗ σ₂₃ ∘ₛₗ ↑L

I reinstated the old lemma.

[themathqueen]

what happened here?

[themathqueen]

Suggested change