Theorems · Theorem · logic and foundations
Nat.Subtype.ofNat_range
∀ {s : Set ℕ} [inst : Infinite ↑s] [inst_1 : DecidablePred fun x => x ∈ s], Set.range (Nat.Subtype.ofNat s) = Set.univ- Defined in
- Mathlib.Logic.Denumerable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- InfiniteDecidablePred
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement · cited by 4,705
- Set.univstatement · cited by 3,945
- Infinitestatement and proof · cited by 352
- Function.Surjective.range_eqproof · cited by 70
- Nat.Subtype.ofNatstatement · cited by 9
- Nat.Subtype.ofNat_surjectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Subtype.coe_comp_ofNat_rangeproof · cited by 2