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Metatheorem resolving all consequences of Equation1571 #341

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merged 16 commits into from
Oct 7, 2024

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franklindyer
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@franklindyer franklindyer commented Oct 5, 2024

This is some intermediate work as I work towards #221, which involves a special case of commutative semigroups. But it also includes some metatheorems that could be generally useful for working with associativity.

Includes:

  • a convenience function for fully right-associating any operation tree when the operation is associative
  • definition and Magma instance of a free semigroup
  • proof that evaluation in any semigroup is a homomorphism
  • proof that the variable names can be sorted in a free semigroup expression without affecting the evaluated value, so long as the codomain semigroup is commutative
  • all of this is combined to write a metatheorem ProveEquation1571Consequence that should be capable of automatically proving any consequence of Equation1571

Any revisions to shorten my proofs or make the naming/notation more convenient is welcome :-)

@franklindyer franklindyer changed the title Free semigroup definition and some useful utilities Metatheorem resolving all consequences of Equation1571 Oct 7, 2024
@pitmonticone pitmonticone self-assigned this Oct 7, 2024
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pitmonticone commented Oct 7, 2024

Thanks! I will review it later.

@pitmonticone pitmonticone added the awaiting-review the PR passes CI and is ready for review label Oct 7, 2024
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Thanks @franklindyer! I have just golfed the new proofs in Subgraph.lean.

Let's wait for the CI and then I'll merge.

@pitmonticone pitmonticone removed the awaiting-review the PR passes CI and is ready for review label Oct 7, 2024
@pitmonticone pitmonticone merged commit a9301dc into teorth:main Oct 7, 2024
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2 participants