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Theorems · Theorem · logic and foundations

Cardinal.IsRegular.ne_zero

∀ {c : Cardinal.{u_1}}, c.IsRegular → c ≠ 0

If c is a regular cardinal, then c.ord.ToType has a least element.

Defined in
Mathlib.SetTheory.Cardinal.Regular
Cited by
1 results in Mathlib
Foundations
Depth 73 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.

CategoryTheory.MorphismProperty.isRightAdjoint_ι_isLocal · cited by 1MorphismProperty.isRightA…Cardinal · cited by 2598CardinalLT.lt.ne' · cited by 1417lt.ne'Cardinal.IsRegular · cited by 282Cardinal.IsRegularCardinal.IsRegular.pos · cited by 2IsRegular.posIsRegular.ne_zeroCITED BYCITES

Cites4

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

Cited by1

Results whose statement or proof uses this declaration.