feat(SetTheory/Ordinal): definition of addition and multiplication

[plp127]

We prove theorems Ordinal.type_lt_sum_lex and Ordinal.type_lt_prod_lex, which characterize addition and multiplication on ordinals.

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[github-actions]

PR summary 2dc352391d

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)

+ instance [LT α] [LT β] [WellFoundedGT α] [WellFoundedGT β] : WellFoundedGT (α ⊕ₗ β) := by
+ instance [LT α] [LT β] [WellFoundedLT α] [WellFoundedLT β] : WellFoundedLT (α ⊕ₗ β)
+ lex_flip_iff
+ type_lt_prod_lex
+ type_lt_sum_lex
+ type_lt_withBot
+ type_lt_withTop

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 2dc3523).

• +7 new declarations
• −0 removed declarations

+Ordinal.type_lt_prod_lex
+Ordinal.type_lt_sum_lex
+Ordinal.type_lt_withBot
+Ordinal.type_lt_withTop
+Sum.Lex.instWellFoundedGTLex
+Sum.Lex.instWellFoundedLTLex
+Sum.lex_flip_iff

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

Current commit 2dc352391d
Reference commit a6e849c904

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).

[vihdzp]

I can't believe we didn't have any of this!