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Theorems · Definition · combinatorics

Matroid.freeOn

{α : Type u_1} → Set α → Matroid α

The Matroid α with ground set E whose only base is E.

Defined in
Mathlib.Combinatorics.Matroid.Constructions
Cited by
25 results in Mathlib
Foundations
Depth 79 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.uniqueBaseOn · cited by 17Matroid.uniqueBaseOnMatroid.freeOn_indep_iff · cited by 5Matroid.freeOn_indep_iffMatroid.freeOn_ground · cited by 3Matroid.freeOn_groundMatroid.freeOn_indep · cited by 3Matroid.freeOn_indepMatroid.uniqueBaseOn_inter_ground_eq · cited by 2Matroid.uniqueBaseOn_inte…Matroid.freeOn_closure_eq · cited by 2Matroid.freeOn_closure_eqMatroid.uniqueBaseOn_closure_eq · cited by 1Matroid.uniqueBaseOn_clos…Matroid.uniqueBaseOn_self · cited by 1Matroid.uniqueBaseOn_selfMatroid.freeOn_dual_eq · cited by 1Matroid.freeOn_dual_eqMatroid.loopyOn_dual_eq · cited by 1Matroid.loopyOn_dual_eqMatroid.freeOn_isBasis'_iff · cited by 1Matroid.freeOn_isBasis'_i…Matroid.freeOn_isBasis_iff · cited by 1Matroid.freeOn_isBasis_iffMatroid.eq_freeOn_iff · cited by 1Matroid.eq_freeOn_iffMatroid.freeOn_restrict · cited by 1Matroid.freeOn_restrictMatroid.restrict_eq_freeOn_iff · cited by 1Matroid.restrict_eq_freeO…Set · cited by 53352SetMatroid · cited by 1258MatroidMatroid.dual · cited by 79Matroid.dualMatroid.loopyOn · cited by 32Matroid.loopyOnMatroid.freeOnCITED BYCITES

Cites4

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

Cited by26

Results whose statement or proof uses this declaration.