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Theorems · Theorem · combinatorics

Matroid.IsCircuit.eq_of_subset_isCircuit

∀ {α : Type u_1} {M : Matroid α} {C C' : Set α}, M.IsCircuit C → M.IsCircuit C' → C ⊆ C' → C = C'
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.IsLoop.eq_of_isCircuit_mem · cited by 2IsLoop.eq_of_isCircuit_memMatroid.IsCircuit.eq_of_superset_isCircuit · cited by 1IsCircuit.eq_of_superset_…Matroid.IsCircuit.elimination · cited by 0IsCircuit.eliminationSet · cited by 53352SetMatroid · cited by 1258MatroidMatroid.IsCircuit · cited by 108Matroid.IsCircuitMatroid.IsCircuit.dep · cited by 15IsCircuit.depMatroid.IsCircuit.eq_of_dep_subset · cited by 3IsCircuit.eq_of_dep_subsetIsCircuit.eq_of_subset_isCirc…CITED BYCITES

Cites5

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.