[Merged by Bors] - feat(Order): characterise compact elements in atomistic lattices

[YaelDillies]

... as those elements that are the suprema of finitely many atoms.

Also make the type variable correctly implicit in most lemmas and move declarations out of the CompleteLattice namespace.

---

[github-actions]

PR summary 37c7056e66

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ IsAtom.isCompactElement
+ IsCompactElement.exists_finite_isAtom
+ IsCompactElement.iSup
+ IsCompactElement.sSup
+ isCompactElement_iff_exists_finite_isAtom

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.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 37c7056).

• +24 new declarations
• −19 removed declarations

-CompleteLattice.IsCompactElement.directed_sSup_lt_of_lt
-CompleteLattice.IsCompactElement.exists_finset_of_le_iSup
-CompleteLattice.IsSupClosedCompact
-CompleteLattice.IsSupClosedCompact.isSupFiniteCompact
-CompleteLattice.IsSupClosedCompact.wellFoundedGT
-CompleteLattice.IsSupFiniteCompact
-CompleteLattice.IsSupFiniteCompact.isSupClosedCompact
-CompleteLattice.IsSupFiniteCompact.wellFoundedGT
-CompleteLattice.WellFoundedGT.isSupClosedCompact
-CompleteLattice.WellFoundedGT.isSupFiniteCompact
-CompleteLattice.isCompactElement_finsetSup
-CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSup
-CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup
-CompleteLattice.isCompactElement_iff_le_of_directed_sSup_le
-CompleteLattice.isSupClosedCompact_iff_wellFoundedGT
-CompleteLattice.isSupFiniteCompact_iff_all_elements_compact
-CompleteLattice.isSupFiniteCompact_iff_isSupClosedCompact
-CompleteLattice.wellFoundedGT_characterisations
-CompleteLattice.wellFoundedGT_iff_isSupFiniteCompact
+IsAtom.isCompactElement
+IsCompactElement.directed_sSup_lt_of_lt
+IsCompactElement.exists_finite_isAtom
+IsCompactElement.exists_finset_of_le_iSup
+IsCompactElement.iSup
+IsCompactElement.sSup
+IsSupClosedCompact
+IsSupClosedCompact.isSupFiniteCompact
+IsSupClosedCompact.wellFoundedGT
+IsSupFiniteCompact
+IsSupFiniteCompact.isSupClosedCompact
+IsSupFiniteCompact.wellFoundedGT
+WellFoundedGT.isSupClosedCompact
+WellFoundedGT.isSupFiniteCompact
+isCompactElement_finsetSup
+isCompactElement_iff_exists_finite_isAtom
+isCompactElement_iff_exists_le_iSup_of_le_iSup
+isCompactElement_iff_exists_le_sSup_of_le_sSup
+isCompactElement_iff_le_of_directed_sSup_le
+isSupClosedCompact_iff_wellFoundedGT
+isSupFiniteCompact_iff_all_elements_compact
+isSupFiniteCompact_iff_isSupClosedCompact
+wellFoundedGT_characterisations
+wellFoundedGT_iff_isSupFiniteCompact

---

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

Current commit 37c7056e66
Reference commit 0383a80e64

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.py 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).

[eric-wieser]

maintainer delegate

(CI is still broken)

[github-actions]

🚀 Pull request has been placed on the maintainer queue by eric-wieser.

[jcommelin]

Thanks 🎉

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-Build Step
• ci (staging) / Lint style
• ci (staging) / Post-CI job
• ci (staging) / Build
• ci (staging) / Test and lint