25 lines
888 B
Text
25 lines
888 B
Text
import data.finset data.finset.card data.finset.equiv
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open nat decidable
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namespace finset
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variable {A : Type}
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open finset (to_nat)
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open finset (of_nat)
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private lemma of_nat_eq_insert : ∀ {n s : nat}, n ∉ of_nat s → of_nat (2^n + s) = insert n (of_nat s)
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| 0 s h := sorry
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| (succ n) s h :=
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have n ∉ of_nat s, from sorry,
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assert of_nat s = insert n (of_nat s), from sorry,
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finset.ext (λ x,
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have gen : ∀ m, m ∈ of_nat (2^(succ n) + s) ↔ m ∈ insert (succ n) (of_nat s)
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| zero :=
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assert aux₁ : odd (2^(succ n) + s) ↔ odd s, from sorry,
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calc
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0 ∈ of_nat (2^(succ n) + s) ↔ odd (2^(succ n) + s) : sorry
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... ↔ odd s : aux₁
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... ↔ 0 ∈ insert (succ n) (of_nat s) : sorry
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| (succ m) := sorry,
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gen x)
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end finset
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