Theorems · Theorem · combinatorics
Set.infinite_coe_iff
∀ {α : Type u} {s : Set α}, Infinite ↑s ↔ s.Infinite- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 7,166
- Iff.notproof · cited by 489
- Infinitestatement · cited by 352
- Set.Infinitestatement · cited by 263
- Set.finite_coe_iffproof · cited by 21
- not_finite_iff_infiniteproof · cited by 8
Cited by16
Results whose statement or proof uses this declaration.
- Set.Infinite.to_subtypeproof · cited by 19
- Set.Ioi_infiniteproof · cited by 5
- Set.not_injOn_infinite_finite_imageproof · cited by 4
- Set.Ioo_infiniteproof · cited by 3
- exists_increasing_or_nonincreasing_subseq'proof · cited by 1
- Algebraic.aleph0_le_cardinalMk_of_charZeroproof · cited by 1
- ENNReal.tsum_set_oneproof · cited by 1
- Set.Ioc.infiniteproof · cited by 0
- AddCircle.card_addOrderOf_eq_totientproof · cited by 0
- Set.Iio_infiniteproof · cited by 0
- Set.Icc.infiniteproof · cited by 0
- Set.Iic_infiniteproof · cited by 0