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feat(algebra/order): allow simp to flip inequalities #1418

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merged 2 commits into from
Sep 10, 2019

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semorrison
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@semorrison semorrison commented Sep 9, 2019

We have a constant problem that while a > b is definitionally equal to b < a, tactics that work at the syntactic level can't see this.

This change introduces two simp lemmas, rewriting > and in terms of < and . This requires a few tweaks elsewhere (essentially places where simp now finishes or comes closer to finishing).

Later, I would like to

  1. Just do some general cleanup, replacing lots of > with < in basic files.
  2. Start adding @[simp] to many more lemmas about inequalities.
  3. Provide substitutes for the default well_founded tactics, which actually break when simp is too good at inequalities. See feat(well_founded_tactics): patch default_dec_tac #1419.

@semorrison semorrison requested a review from a team as a code owner September 9, 2019 04:20
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avigad commented Sep 9, 2019

This looks good to me. I'll merge in a day or two if there are no objections.

@avigad avigad added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Sep 10, 2019
@mergify mergify bot merged commit 2dd6398 into master Sep 10, 2019
@mergify mergify bot deleted the flipping_inequalities branch September 10, 2019 15:34
anrddh pushed a commit to anrddh/mathlib that referenced this pull request May 15, 2020
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