feat(CategoryTheory/Limits/Shapes/Preorder): principal segments

[joelriou]

In the study of well order continuous functors, we now use the initial/principal segment API from order theory.

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[github-actions]

PR summary 97a7aca2cf

Import changes exceeding 2%

%	File
+2.35%	Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous
+2.34%	Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous	469	480	+11 (+2.35%)
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting	471	482	+11 (+2.34%)
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape	598	608	+10 (+1.67%)

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape	10
3 files Mathlib.CategoryTheory.Limits.Shapes.Preorder.WellOrderContinuous Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting	11
Mathlib.Order.Interval.Set.InitialSeg (new file)	382
Mathlib.CategoryTheory.Limits.Shapes.Preorder.PrincipalSeg (new file)	430

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Declarations diff

+ PrincipalSeg.cocone
+ PrincipalSeg.orderIsoIio
+ hasColimitsOfShape_of_initialSeg
+ hasColimitsOfShape_of_isSuccLimit'
+ hasIterationOfShape_of_initialSeg
+ initialSegIic
+ initialSegIicIicOfLE
+ instance (F : J ⥤ C) {J' : Type w'} [PartialOrder J'] (e : J' ≃o J)
+ instance (F : J ⥤ C) {J' : Type w'} [PartialOrder J'] (f : J' ≤i J)
+ isColimitOfIsWellOrderContinuous'
+ principalSegIio
+ principalSegIioIicOfLE
+ principalSegIioIicOfLE_toRelEmbedding
- coconeLT
- restrictionLT

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/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).