Theorems · Theorem · combinatorics
SimpleGraph.card_interedges_add_card_interedges_compl
∀ {α : Type u_4} (G : SimpleGraph α) [inst : DecidableRel G.Adj] {s t : Finset α} [inst_1 : DecidableEq α],
Disjoint s t → (G.interedges s t).card + (Gᶜ.interedges s t).card = s.card * t.card- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableRelDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- SimpleGraphstatement and proof · cited by 3,072
- Compl.complstatement and proof · cited by 2,925
- Finset.cardstatement and proof · cited by 2,327
- Disjointstatement and proof · cited by 2,201
- SProd.sprodproof · cited by 1,750
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterproof · cited by 949
- Finset.filter_congrproof · cited by 167
- Finset.mem_productproof · cited by 48
- Finset.card_productproof · cited by 39
- Finset.card_union_of_disjointproof · cited by 37
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.edgeDensity_add_edgeDensity_complproof · cited by 0