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Theorems · Theorem · combinatorics

Matroid.IsCircuit.nonempty

∀ {α : Type u_1} {M : Matroid α} {C : Set α}, M.IsCircuit C → C.Nonempty
Defined in
Mathlib.Combinatorics.Matroid.Circuit
Cited by
3 results in Mathlib
Foundations
Depth 63 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.

Matroid.IsCocircuit.nonempty · cited by 0IsCocircuit.nonemptyMatroid.loopless_iff_forall_isCircuit · cited by 0Matroid.loopless_iff_fora…Matroid.empty_not_isCircuit · cited by 0Matroid.empty_not_isCircu…Set · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptyMatroid · cited by 1258MatroidMatroid.IsCircuit · cited by 108Matroid.IsCircuitMatroid.IsCircuit.dep · cited by 15IsCircuit.depMatroid.Dep.nonempty · cited by 1Dep.nonemptyIsCircuit.nonemptyCITED BYCITES

Cites6

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

Cited by3

Results whose statement or proof uses this declaration.