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Theorems · Theorem · logic and foundations

Cardinal.IsInaccessible.aleph_ord

∀ {c : Cardinal.{u_1}}, c.IsInaccessible → Cardinal.aleph c.ord = c
Defined in
Mathlib.SetTheory.Cardinal.Regular
Cited by
2 results in Mathlib
Foundations
Depth 102 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.

Cardinal.IsInaccessible.omega_ord · cited by 1IsInaccessible.omega_ordCardinal.aleph_univ · cited by 0Cardinal.aleph_univDFunLike.coe · cited by 62936DFunLike.coeLE.le.trans · cited by 3151le.transCardinal · cited by 2598CardinalOrdinal · cited by 1688OrdinalOrderEmbedding · cited by 619OrderEmbeddingEq.le · cited by 605Eq.leLE.le.antisymm · cited by 507le.antisymmCardinal.ord · cited by 266Cardinal.ordCardinal.aleph · cited by 76Cardinal.alephStrictMono.comp · cited by 36StrictMono.compStrictMono.le_apply · cited by 32StrictMono.le_applyOrderEmbedding.strictMono · cited by 26OrderEmbedding.strictMonoCardinal.IsInaccessible · cited by 18Cardinal.IsInaccessibleCardinal.ord_strictMono · cited by 7Cardinal.ord_strictMonoCardinal.aleph_le_beth · cited by 3Cardinal.aleph_le_bethIsInaccessible.aleph_ordCITED BYCITES

Cites16

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.