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feat(tactic/positivity): Handle a ≠ 0 goals #16483

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Add some light postprocessing for positivity to prove goals of the form 0 ≠ a and a ≠ 0 when it can derive 0 < a.


The motivation for this is that side goals of order lemmas are sometimes a ≠ 0 because they hold for both 0 < a and a < 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 handle a ≠ 0 hypotheses (rather than a simple postprocessing) by changing strictness to

meta inductive strictness : Type
| positive : expr → strictness
| nonnegative : expr → strictness
| nonzero : expr → strictness

This 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.

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@YaelDillies YaelDillies added awaiting-review The author would like community review of the PR t-meta Tactics, attributes or user commands t-algebra Algebra (groups, rings, fields etc) t-order Order hierarchy labels Sep 12, 2022
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Closing in favor of #16529.

@YaelDillies YaelDillies closed this Oct 4, 2022
@YaelDillies YaelDillies deleted the positivity_ne_zero branch November 9, 2022 16:05
@YaelDillies YaelDillies removed the awaiting-review The author would like community review of the PR label Feb 27, 2023
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