Theorems · Theorem · combinatorics
Graph.isLink_iff_inc
∀ {α : Type u_1} {β : Type u_2} {x y : α} {e : β} {G : Graph α β},
G.IsLink e x y ↔ G.Inc e x ∧ G.Inc e y ∧ ∀ (z : α), G.Inc e z → z = x ∨ z = yThe binary incidence predicate can be expressed in terms of the unary one.
- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Graphstatement and proof · cited by 242
- Graph.IsLinkstatement and proof · cited by 124
- Graph.Incstatement and proof · cited by 42
- Graph.IsLink.symmproof · cited by 11
- Graph.IsLink.inc_leftproof · cited by 8
- Graph.IsLink.left_eq_or_eqproof · cited by 7
- Graph.Inc.eq_or_eq_of_isLinkproof · cited by 3
- Graph.IsLink.inc_rightproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Graph.inc_eq_inc_iff_isLink_eq_isLinkproof · cited by 0