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Theorems · Inductive type · logic and foundations

Cardinal.IsSingular

Cardinal.{u_1} → Prop

A cardinal is singular if it is infinite and not regular.

Defined in
Mathlib.SetTheory.Cardinal.Regular
Cited by
21 results in Mathlib
Foundations
Depth 19 from the axioms · uses Quot.sound
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Around this declaration

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

Cardinal.isRegular_or_isSingular · cited by 3Cardinal.isRegular_or_isS…Cardinal.IsRegular.not_isSingular · cited by 3IsRegular.not_isSingularCardinal.IsSingular.aleph0_le · cited by 3IsSingular.aleph0_leCardinal.isSingular_aleph_iff · cited by 2Cardinal.isSingular_aleph…Cardinal.isSingular_iff · cited by 2Cardinal.isSingular_iffCardinal.IsSingular.casesOn · cited by 1IsSingular.casesOnCardinal.IsSingular.cof_ord_lt · cited by 1IsSingular.cof_ord_ltCardinal.IsSingular.cof_ord_ne · cited by 1IsSingular.cof_ord_neCardinal.IsSingular.natCast_lt · cited by 1IsSingular.natCast_ltCardinal.IsSingular.not_isRegular · cited by 1IsSingular.not_isRegularCardinal.IsSingular.pos · cited by 1IsSingular.posCardinal.not_isSingular_succ · cited by 1Cardinal.not_isSingular_s…Cardinal.isSingular_aleph_omega0 · cited by 0Cardinal.isSingular_aleph…Cardinal.lt_aleph0_or_isRegular_or_isSingular · cited by 0Cardinal.lt_aleph0_or_isR…Cardinal.IsRegular.of_not_isSingular · cited by 0IsRegular.of_not_isSingul…Cardinal · cited by 2598CardinalCardinal.IsSingularCITED BYCITES

Cites1

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

Cited by23

Results whose statement or proof uses this declaration.