feat(order): finite preorders have finite order dimension#92
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kernelpanic888 wants to merge 1 commit into
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feat(order): finite preorders have finite order dimension#92kernelpanic888 wants to merge 1 commit into
kernelpanic888 wants to merge 1 commit into
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Add instance for finite dimensional order in finite nonempty preorders.
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Add an instance showing that every finite nonempty preorder has finite order dimension.
Addresses the first proposed result in #90.
The
Nonempty αassumption is necessary:FiniteDimensionalOrder αimpliesNonempty α, whileFin 0is finite and has a preorder.The proof assumes an arbitrarily long strict chain, chooses one of length
Fintype.card α, and contradicts the existing boundLTSeries.length_lt_card.Validation:
lake build Mathlib.Order.RelSeriesFin 0counterexample#print axioms Finite.to_finiteDimensionalOrder:propext,Classical.choice,Quot.sound