[Merged by Bors] - feat: lemmas on ordinal exponentiation/logarithms

[vihdzp]

Downstreamed from the CGT repo.

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[github-actions]

PR summary ecdcc43a7a

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

+ div_two_opow_log
+ lt_omega0_omega0_opow
+ one_lt_opow
+ one_lt_pow
+ opow_mul_lt_opow
+ two_opow_log_add

You can run this locally as follows

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

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

The doc-module for scripts/pr_summary/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/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).

[b-mehta]

I'm slightly worried that soon we'll also get lt_omega0_omega0_omega0_opow... Do these have some nice generalisation we could give?

[vihdzp]

ω^ω^x is relevant to me because of the property that a, b < ω^ω^x imply a * b < ω^ω^x. I don't think I have any use for talking about ω^ω^ω^x; maybe it's best to defer any generalizing until that happens.

[b-mehta]

let's hope no-one else has use for that either!

[b-mehta]

oh I see, the point is that being multiplicatively principal is useful enough to deserve extra theorems?

[vihdzp]

Well, it's not that it "deserves" extra theorems, I do actually make use of it!
vihdzp/combinatorial-games#360

[b-mehta]

Oh you mean with natural multiplication, I see

[vihdzp]

It's closed under both kinds of multiplication, in fact :)
And nimber multiplication too!

[b-mehta]

It's closed under both kinds of multiplication, in fact :)

Right, but being closed under ordinal multiplication is already in mathlib so you can't be using this to prove that (which is what I thought you meant before clicking the link)

[b-mehta]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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• ci (staging) / Post-Build Step