Mathlib Map

Theorems · Theorem · logic and foundations

Cardinal.lt_lift_iff

∀ {a : Cardinal.{u}} {b : Cardinal.{max u v}}, b < Cardinal.lift.{v, u} a ↔ ∃ a' < a, Cardinal.lift.{v, u} a' = b
Defined in
Mathlib.SetTheory.Cardinal.Order
Cited by
4 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cardinal.lt_aleph0 · cited by 19Cardinal.lt_aleph0Cardinal.lift_succ · cited by 4Cardinal.lift_succCardinal.lt_univ' · cited by 3Cardinal.lt_univ'Module.exists_set_linearIndependent_of_lt_lift_rank · cited by 2Module.exists_set_linearI…Cardinal · cited by 2598CardinalCardinal.lift · cited by 583Cardinal.liftCardinal.liftInitialSeg · cited by 8Cardinal.liftInitialSegInitialSeg.lt_apply_iff · cited by 3InitialSeg.lt_apply_iffCardinal.lt_lift_iffCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.