50 lines
1.3 KiB
Text
50 lines
1.3 KiB
Text
import data.finset
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open finset list
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example (A : Type) (f : nat → nat → nat → nat) (a b : nat) : a = b → f a = f b :=
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begin
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intros,
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congruence,
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assumption
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end
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structure finite_set [class] {T : Type} (xs : set T) :=
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(to_finset : finset T) (is_equiv : to_set to_finset = xs)
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definition finset_set.is_subsingleton [instance] (T : Type) (xs : set T) : subsingleton (finite_set xs) :=
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begin
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constructor, intro a b,
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induction a with f₁ h₁,
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induction b with f₂ h₂,
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subst xs,
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let e := to_set.inj h₂,
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subst e
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end
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open finite_set
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definition card {T : Type} (xs : set T) [fxs : finite_set xs] :=
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finset.card (to_finset xs)
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example (A : Type) (s₁ s₂ : set A) [fxs₁ : finite_set s₁] [fxs₂ : finite_set s₂] : s₁ = s₂ → card s₁ = card s₂ :=
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begin
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intros,
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congruence,
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unfold set at *,
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assumption
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end
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example {A : Type} (l₁ l₂ : list A) (h₁ : l₁ ≠ []) (h₂ : l₂ ≠ []) : l₁ = l₂ → last l₁ h₁ = last l₂ h₂ :=
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begin
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intros,
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congruence,
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assumption
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end
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example (A : Type) (last₁ last₂ : Π l : list A, l ≠ [] → A) (l₁ l₂ : list A) (h₁ : l₁ ≠ []) (h₂ : l₂ ≠ []) :
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last₁ = last₂ → l₁ = l₂ → last₁ l₁ h₁ = last₂ l₂ h₂ :=
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begin
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intro e₁ e₂,
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congruence,
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repeat assumption
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end
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