Theorems · Theorem · logic and foundations
Cardinal.preBeth_lt_preBeth
∀ {o₁ o₂ : Ordinal.{u_1}}, Cardinal.preBeth o₁ < Cardinal.preBeth o₂ ↔ o₁ < o₂- Defined in
- Mathlib.SetTheory.Cardinal.Aleph
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- StrictMono.lt_iff_ltproof · cited by 86
- Cardinal.preBethstatement · cited by 31
- Cardinal.preBeth_strictMonoproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.isStrongPrelimit_preBethproof · cited by 1
- Cardinal.preBeth_posproof · cited by 0