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Theorems · Theorem · logic and foundations

Ordinal.isPrincipal_add_ord

∀ {c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c → Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) c.ord
Defined in
Mathlib.SetTheory.Cardinal.Ordinal
Cited by
2 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Ordinal.IsInitial.isPrincipal_add · cited by 2IsInitial.isPrincipal_addOrdinal.principal_add_ord · cited by 0Ordinal.principal_add_ordCardinal · cited by 2598CardinalOrdinal · cited by 1688OrdinalCardinal.aleph0 · cited by 521Cardinal.aleph0Cardinal.ord · cited by 266Cardinal.ordOrdinal.IsPrincipal · cited by 92Ordinal.IsPrincipalCardinal.lt_ord · cited by 13Cardinal.lt_ordCardinal.add_lt_of_lt · cited by 7Cardinal.add_lt_of_ltOrdinal.card_add · cited by 6Ordinal.card_addOrdinal.isPrincipal_add_ordCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.