Theorems · Theorem · combinatorics
Graph.IsNonloopAt.not_isLoopAt
∀ {α : Type u_1} {β : Type u_2} {x : α} {e : β} {G : Graph α β}, G.IsNonloopAt e x → ∀ (y : α), ¬G.IsLoopAt e y- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsLoopAtstatement and proof · cited by 29
- Graph.IsNonloopAtstatement and proof · cited by 16
- Graph.IsLoopAt.not_isNonloopAtproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Graph.isNonloopAt_iff_inc_not_isLoopAtproof · cited by 0