[Merged by Bors] - feat: =, ≠, <, and ≤ functionality for norm_num
#1568
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* use `norm_num1` throughout * new tests for eq/neq functionality * comment out tests which were being done by `simp`
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≠ functionality for norm_num=, ≠, <, and ≤ functionality for norm_num
* use LinearOrderedRing for rat theorems
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This PR gives `norm_num` basic inequality (and equality) functionality (towards #1567), including the following: ``` example {α} [DivisionRing α] [CharZero α] : (-1:α) ≠ 2 := by norm_num ``` We implement basic logical extensions to handle `=` and `≠` together, namely `¬`, `True`, and `False`. `≠` is not given an extension, as it is handled by `=` and `¬`. For now we only can prove `≠` for numbers given a `CharZero α` instance. - [x] depends on: #1578 Co-authored-by: Mario Carneiro <di.gama@gmail.com>
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=, ≠, <, and ≤ functionality for norm_num=, ≠, <, and ≤ functionality for norm_num
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This PR gives
norm_numbasic inequality (and equality) functionality (towards #1567), including the following:We implement basic logical extensions to handle
=and≠together, namely¬,True, andFalse.≠is not given an extension, as it is handled by=and¬.For now we only can prove
≠for numbers given aCharZero αinstance.