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Theorems · Theorem · combinatorics

FinEnum.card_pos_iff

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

A type indexable by Fin n with positive n is inhabited and vice versa.

Defined in
Mathlib.Data.FinEnum
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FinEnum
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FinEnum.card_pos · cited by 1FinEnum.card_posFinEnum.card · cited by 32FinEnum.cardFintype.card_pos_iff · cited by 31Fintype.card_pos_iffFinEnum · cited by 21FinEnumFinEnum.card_eq_fintypeCard · cited by 4FinEnum.card_eq_fintypeCa…FinEnum.card_pos_iffCITED BYCITES

Cites4

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Cited by1

Results whose statement or proof uses this declaration.