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[Merged by Bors] - refactor: define < on WithBot/WithTop as an inductive predicate#30848

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[Merged by Bors] - refactor: define < on WithBot/WithTop as an inductive predicate#30848
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@YaelDillies YaelDillies commented Oct 24, 2025

Follow up to #19668, where I did the same for LE but forgot to do it for LT.

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@github-actions github-actions bot added the t-order Order theory label Oct 24, 2025
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github-actions bot commented Oct 24, 2025 •
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PR summary 6c19380648

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ LT
+ instance (priority := 10) instLT : LT (WithBot α) where lt := WithBot.LT
+ instance (priority := 10) instLT : LT (WithTop α) where lt a b := WithBot.LT (α := αᵒᵈ) b a
+++ lt_iff_exists
+++--- lt_def
+--+ lt_coe_iff
- instance (priority := 10) instLT : LT (WithBot α)
- instance (priority := 10) instLT : LT (WithTop α)

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.

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).

@grunweg grunweg added the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Oct 24, 2025
@github-actions github-actions bot removed the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Oct 24, 2025
b-mehta
b-mehta reviewed Oct 25, 2025
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vihdzp
vihdzp reviewed Oct 25, 2025
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Mathlib/Order/WithBot.lean
Equivalently, `x ≤ y` can be defined as `∀ a : α, x = ↑a → ∃ b : α, y = ↑b ∧ a ≤ b`,
see `le_if_forall`. The definition as an inductive predicate is preferred since it
cannot be accidentally unfolded too far. -/
/-- Auxiliary definition for the order on `WithBot`. -/
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@vihdzp vihdzp Oct 25, 2025

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If this is auxiliary, why not just private it?

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@YaelDillies YaelDillies Oct 25, 2025

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because that messes up with mk_iff unfortunately

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@JovanGerb JovanGerb Oct 26, 2025

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But surely there is the advantage of allowing people to use the cases tactic on this inductive? Is it really an implementation detail?

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@YaelDillies YaelDillies Oct 26, 2025

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No, not really. You're right, I forgot to mention that. I think it's good for it not to be private

@YaelDillies
refactor: define < on WithBot/WithTop as an inductive predicate
5fcd699 
Follow up to leanprover-community#19668, where I did the same for `LE` but forgot to do it for `LT`.
@YaelDillies YaelDillies force-pushed the with_bot_inductive_lt branch from 5e41ad9 to 5fcd699 Compare October 28, 2025 17:25
Vierkantor
Vierkantor approved these changes Nov 3, 2025
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Thanks!

bors merge

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Nov 3, 2025
mathlib-bors bot pushed a commit that referenced this pull request Nov 3, 2025
@YaelDillies
refactor: define < on WithBot/WithTop as an inductive predicate (…
d2abc00 
…#30848)

Follow up to #19668, where I did the same for `LE` but forgot to do it for `LT`.
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mathlib-bors bot commented Nov 3, 2025

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title refactor: define < on WithBot/WithTop as an inductive predicate [Merged by Bors] - refactor: define < on WithBot/WithTop as an inductive predicate Nov 3, 2025
@mathlib-bors mathlib-bors bot closed this Nov 3, 2025
@YaelDillies YaelDillies deleted the with_bot_inductive_lt branch November 3, 2025 17:49
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