feat(tactic/positivity): Handle a ≠ 0
goals
#16483
Closed
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Add some light postprocessing for
positivity
to prove goals of the form0 ≠ a
anda ≠ 0
when it can derive0 < a
.The motivation for this is that side goals of order lemmas are sometimes
a ≠ 0
because they hold for both0 < a
anda < 0
.This is only a fraction of what can be done in this direction. If you're happy with this, I will then make
positivity
fully handlea ≠ 0
hypotheses (rather than a simple postprocessing) by changingstrictness
toThis still works on a design level because there's a unique meaningful way of combining any two
≤
,<
,≠
results. In particular, there won't be any branching.