28 lines
780 B
Text
28 lines
780 B
Text
import data.finset
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open subtype setoid finset set
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inductive finite_set [class] {T : Type} (xs : set T) :=
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| mk : ∀ (fxs : finset T), to_set fxs = xs → finite_set xs
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definition card {T : Type} (xs : set T) [fn : finite_set xs] : nat :=
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begin
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induction fn,
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exact finset.card fxs
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end
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example {T : Type} (xs : set T) [fn₁ : finite_set xs] [fn₂ : finite_set xs] : @card T xs fn₁ = @card T xs fn₂ :=
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begin
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induction fn₁ with fxs₁ h₁,
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induction fn₂ with fxs₂ h₂,
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subst xs,
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apply sorry
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end
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example {T : Type} (xs : set T) [fn₁ : finite_set xs] [fn₂ : finite_set xs] : @card T xs fn₁ = @card T xs fn₂ :=
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begin
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induction fn₁ with fxs₁ h₁,
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induction fn₂ with fxs₂ h₂,
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subst xs,
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note aux := to_set.inj h₂,
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subst aux
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end
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