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Theorems · Theorem · combinatorics

Quiver.shortest_path_spec

∀ {V : Type u} [inst : Quiver V] (r : V) [inst_1 : Quiver.RootedConnected r] {a : V} (p : Quiver.Path r a),
  (Quiver.shortestPath r a).length ≤ p.length

The length of a path is at least the length of the shortest path

Defined in
Mathlib.Combinatorics.Quiver.Arborescence
Cited by
0 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
QuiverQuiver.RootedConnected
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Around this declaration

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Set.univ · cited by 3945Set.univQuiver · cited by 405Quivernot_lt · cited by 306not_ltQuiver.Path · cited by 166Quiver.PathQuiver.Path.length · cited by 39Path.lengthWellFounded.not_lt_min · cited by 20WellFounded.not_lt_minQuiver.RootedConnected · cited by 2Quiver.RootedConnectedQuiver.shortestPath · cited by 2Quiver.shortestPathQuiver.shortest_path_specCITED BYCITES

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