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https://github.com/Smaug123/agdaproofs
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19 lines
706 B
Agda
19 lines
706 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import LogicalFormulae
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open import Functions
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open import Numbers.Naturals.Definition
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open import Sets.FinSet.Definition
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open import Setoids.Setoids
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module Setoids.Cardinality.Infinite.Definition where
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InfiniteSetoid : {a b : _} {A : Set a} (S : Setoid {a} {b} A) → Set (a ⊔ b)
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InfiniteSetoid {A = A} S = (n : ℕ) → (f : FinSet n → A) → (SetoidBijection (reflSetoid (FinSet n)) S f) → False
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record DedekindInfiniteSetoid {a b : _} {A : Set a} (S : Setoid {a} {b} A) : Set (a ⊔ b) where
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field
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inj : ℕ → A
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isInjection : SetoidInjection (reflSetoid ℕ) S inj
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