Theorems · Theorem · combinatorics
SimpleGraph.IsCycles.snd_of_mem_support_of_isPath_of_adj
∀ {V : Type u_1} {G : SimpleGraph V} [Finite V] {v w w' : V},
G.IsCycles → ∀ (p : G.Walk v w), w ≠ w' → w' ∈ p.support → p.IsPath → G.Adj v w' → p.snd = w'- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Finitestatement and proof · cited by 3,029
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.supportstatement and proof · cited by 307
- SimpleGraph.neighborSetproof · cited by 257
- SimpleGraph.Walk.lengthproof · cited by 212
- Set.toFiniteproof · cited by 174
- SimpleGraph.Walk.IsPathstatement and proof · cited by 140
- SimpleGraph.Walk.getVertproof · cited by 114
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