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Theorems · Theorem · logic and foundations

Nat.Subtype.coe_comp_ofNat_range

∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s],
  Set.range (Subtype.val ∘ Nat.Subtype.ofNat s) = s
Defined in
Mathlib.Logic.Denumerable
Cited by
2 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
InfiniteDecidablePred
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Nat.range_nth_of_infinite · cited by 3Nat.range_nth_of_infiniteNat.orderEmbeddingOfSet_range · cited by 1Nat.orderEmbeddingOfSet_r…Set · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.image · cited by 5609Set.imageSet.range · cited by 4705Set.rangeInfinite · cited by 352InfiniteSet.image_univ · cited by 322Set.image_univSet.range_comp · cited by 223Set.range_compSubtype.range_coe · cited by 98Subtype.range_coeNat.Subtype.ofNat · cited by 9Subtype.ofNatNat.Subtype.ofNat_range · cited by 1Subtype.ofNat_rangeSubtype.coe_comp_ofNat_rangeCITED BYCITES

Cites10

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Cited by2

Results whose statement or proof uses this declaration.