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Support lemmas#41

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support-lemmas
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Support lemmas#41
ScriptRaccoon wants to merge 3 commits intomainfrom
support-lemmas

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@ScriptRaccoon ScriptRaccoon commented Apr 9, 2026

The implications in the database have a quite strict format: if a category C has properties P, Q, ..., then it has property X. Even though this covers many results of category theory, some results are slightly different: either because property X is not interesting in its own right, so that it does not "deserve" to be added as a property to the database, or because the conclusion is actually a disjunction, "X or Y". The deduction system does not work with disjunctions (this would blow it up and could also yield non-constructive proofs, which I would like to avoid).

Here is a typical example: if a category is finitary algebraic and thin, then it is trivial or equivalent to {0 < 1}. We do not want to add the property "is equivalent to {0 < 1}" to the database, since it is not interesting in its own right (and probably has no name either).

Also, some results touch many categorical structures at once. They make some conclusions about a category based on the existence of functors with some properties.

Lemmas try to solve this issue by allowing results in arbitrary formats. They have no strict relationships with other data in the database, i.e., the lemmas table has no foreign keys. In the future, they might be replaced with entities that do have proper relationships.

Lemmas can be referenced in manual property assignments to avoid repeating arguments. For example, the result about thin finitary algebraic categories above can be used to show that the three categories N_oo, walking_commutative_square, and walking_composable_pair are not finitary algebraic.

I want to use Lemmas in particular to avoid duplicating proofs.

WIP. More lemmas will be added soon in this PR.

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