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Theorems · Theorem · combinatorics

FinEnum.card_pos

∀ {α : Type u_1} [inst : FinEnum α] [Nonempty α], 0 < FinEnum.card α

Any non-empty enumeration has more than one element.

Defined in
Mathlib.Data.FinEnum
Cited by
1 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FinEnumNonempty
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FinEnum.card_ne_zero · cited by 0FinEnum.card_ne_zeroFinEnum.card · cited by 32FinEnum.cardFinEnum · cited by 21FinEnumFinEnum.card_pos_iff · cited by 1FinEnum.card_pos_iffFinEnum.card_posCITED BYCITES

Cites3

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.