Theorems · Theorem · logic and foundations
Cardinal.mk_embedding_eq_zero_iff_lift_lt
∀ {α : Type u} {β' : Type v},
Cardinal.mk (α ↪ β') = 0 ↔ Cardinal.lift.{u, v} (Cardinal.mk β') < Cardinal.lift.{v, u} (Cardinal.mk α)- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Cardinalstatement · cited by 2,598
- Function.Embeddingstatement · cited by 988
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- not_leproof · cited by 328
- not_nonempty_iffproof · cited by 20
- Cardinal.lift_mk_le'proof · cited by 20
- Cardinal.mk_eq_zero_iffproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.mk_embedding_eq_zero_iff_ltproof · cited by 0