mathlib documentation

logic.equiv.nat

Equivalences involving #

This file defines some additional constructive equivalences using encodable and the pairing function on .

An equivalence between bool × ℕ and , by mapping (tt, x) to 2 * x + 1 and (ff, x) to 2 * x.

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An equivalence between ℕ ⊕ ℕ and , by mapping (sum.inl x) to 2 * x and (sum.inr x) to 2 * x + 1.

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An equivalence between and , through ℤ ≃ ℕ ⊕ ℕ and ℕ ⊕ ℕ ≃ ℕ.

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def equiv.prod_equiv_of_equiv_nat {α : Type u_1} (e : α ) :
α × α α

An equivalence between α × α and α, given that there is an equivalence between α and .

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