25 lines
819 B
Lean4
25 lines
819 B
Lean4
import Spa.Lattice
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namespace Spa
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def FiniteHeightLattice.transport {α β : Type*} [Lattice α] [Lattice β]
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[I : FiniteHeightLattice α] (f : α → β) (g : β → α)
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(hf : Monotone f) (hg : Monotone g)
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(hgf : ∀ a, g (f a) = a) (hfg : ∀ b, f (g b) = b) :
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FiniteHeightLattice β where
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bot := f ⊥
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top := f ⊤
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height := I.height
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longestChain :=
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{ series :=
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I.longestChain.series.map f
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(hf.strictMono_of_injective (Function.LeftInverse.injective hgf))
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head_series := congrArg f I.longestChain.head_series
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last_series := congrArg f I.longestChain.last_series
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length_series := I.longestChain.length_series }
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chains_bounded := fun c =>
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I.chains_bounded
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(c.map g (hg.strictMono_of_injective (Function.LeftInverse.injective hfg)))
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end Spa
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