Theorems · Theorem · combinatorics
Sym2.card_toFinset_of_not_isDiag
∀ {α : Type u_1} [inst : DecidableEq α] (z : Sym2 α), ¬z.IsDiag → z.toFinset.card = 2Mapping an unordered pair off the diagonal to a finite set produces a finset of size 2.
- Defined in
- Mathlib.Data.Sym.Sym2
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.cardstatement and proof · cited by 2,327
- Sym2statement and proof · cited by 737
- Sym2.mkproof · cited by 332
- Finset.card_singletonproof · cited by 144
- Sym2.indproof · cited by 66
- Finset.card_insert_of_notMemproof · cited by 45
- Sym2.IsDiagstatement and proof · cited by 43
- Sym2.toFinsetstatement · cited by 10
- Sym2.mk_isDiag_iffproof · cited by 4
- Sym2.toFinset_mk_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.card_toFinset_mem_edgeFinsetproof · cited by 1
- Sym2.card_toFinsetproof · cited by 0