Theorems · Theorem · logic and foundations
Cardinal.mk_compl_of_infinite
∀ {α : Type u_1} [Infinite α] (s : Set α), Cardinal.mk ↑s < Cardinal.mk α → Cardinal.mk ↑sᶜ = Cardinal.mk α- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Compl.complstatement · cited by 2,925
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement and proof · cited by 942
- Infinitestatement and proof · cited by 352
- Cardinal.aleph0_le_mkproof · cited by 32
- Cardinal.mk_sum_complproof · cited by 3
- Cardinal.eq_of_add_eq_of_aleph0_leproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.mk_compl_finset_of_infiniteproof · cited by 0
- Cardinal.extend_function_of_ltproof · cited by 0
- Cardinal.mk_compl_eq_mk_compl_infiniteproof · cited by 0