Theorems · Theorem · logic and foundations
Infinite.of_cardinalMk_le
∀ {α β : Type u} [Infinite α], Cardinal.mk α ≤ Cardinal.mk β → Infinite β- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- 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.infinite_iffproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.exists_infinite_fiber'proof · cited by 1