36 lines
905 B
Lean4
36 lines
905 B
Lean4
import Spa.Lattice.Prod
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import Spa.Lattice.Unit
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namespace Spa
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universe u
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def IterProd (A B : Type u) : ℕ → Type u
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| 0 => B
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| k + 1 => A × IterProd A B k
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namespace IterProd
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variable {A B : Type u}
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instance decidableEq [DecidableEq A] [DecidableEq B] :
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∀ k, DecidableEq (IterProd A B k)
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| 0 => inferInstanceAs (DecidableEq B)
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| k + 1 => @instDecidableEqProd A (IterProd A B k) _ (decidableEq k)
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def build (a : A) (b : B) : (k : ℕ) → IterProd A B k
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| 0 => b
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| k + 1 => (a, build a b k)
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def fixedHeight [FiniteHeightLattice A] [FiniteHeightLattice B] :
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∀ k, FiniteHeightLattice (IterProd A B k)
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| 0 => inferInstanceAs (FiniteHeightLattice B)
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| k + 1 => @Spa.prod A (IterProd A B k) _ (fixedHeight k)
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instance finiteHeight [FiniteHeightLattice A] [FiniteHeightLattice B] (k : ℕ) :
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FiniteHeightLattice (IterProd A B k) := fixedHeight k
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end IterProd
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end Spa
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