Mathlib Map

Theorems · Theorem · combinatorics

Matroid.rankInfinite_iff_aleph0_le_cRank

∀ {α : Type u} {M : Matroid α}, M.RankInfinite ↔ Cardinal.aleph0 ≤ M.cRank
Defined in
Mathlib.Combinatorics.Matroid.Rank.Cardinal
Cited by
1 results in Mathlib
Foundations
Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matroid.toENat_cRank_eq · cited by 1Matroid.toENat_cRank_eqCardinal · cited by 2598CardinalMatroid · cited by 1258MatroidCardinal.aleph0 · cited by 521Cardinal.aleph0not_lt · cited by 306not_ltMatroid.cRank · cited by 17Matroid.cRankMatroid.RankInfinite · cited by 13Matroid.RankInfiniteMatroid.rankFinite_iff_cRank_lt_aleph0 · cited by 3Matroid.rankFinite_iff_cR…Matroid.not_rankFinite_iff · cited by 3Matroid.not_rankFinite_iffMatroid.rankInfinite_iff_alep…CITED BYCITES

Cites8

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.