[Merged by Bors] - feat(tactic/positivity): Handle a ≠ 0 assumptions
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YaelDillies
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| mul_inv_cancel := λ I, fractional_ideal.mul_inv_cancel, | ||
| .. fractional_ideal.comm_semiring } | ||
| .. fractional_ideal.comm_semiring, ..(coe_to_fractional_ideal_injective le_rfl).nontrivial } |
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The simpa call failed because simp now closes the goal thanks to the change to bot_ne_top. It was easier to golf than to fix.
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Make `positivity` handle `a ≠ 0` assumptions. This involves * adding a third constructor to `positivity.strictness`, that I've called `nonzero`. It is meant to hold proofs of `a ≠ 0`, not `0 ≠ a` * modifying the existing extensions to handle that new case. * changing `positivity.orelse'` to account for the fact that if we can prove `0 ≤ a` and `a ≠ 0` then we can prove `0 < a`. * making `compare_hyp` handle `eq` and `ne` hypotheses. ## Other changes * Introduce `tac1 ≤|≥ tac2` as notation for `positivity.orelse' tac1 tac2`. This has the same precedence as the `<|>` notation for `orelse`. * Make `positivity` extensions fail with more informative error messages. This is useless when running `positivity` alone but: * It clearly marks within the code what each failure means * The errors can show up when calling an extension directly. Not sure why you would do that, but you could. * Add a `has_to_format strictness` instance. This is mostly useful for debugging.
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a ≠ 0 assumptionsa ≠ 0 assumptions
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Make
positivityhandlea ≠ 0assumptions. This involvespositivity.strictness, that I've callednonzero. It is meant to hold proofs ofa ≠ 0, not0 ≠ apositivity.orelse'to account for the fact that if we can prove0 ≤ aanda ≠ 0then we can prove0 < a.compare_hyphandleeqandnehypotheses.Other changes
tac1 ≤|≥ tac2as notation forpositivity.orelse' tac1 tac2. This has the same precedence as the<|>notation fororelse.positivityextensions fail with more informative error messages. This is useless when runningpositivityalone but:has_to_format strictnessinstance. This is mostly useful for debugging.