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Theorems · Theorem · combinatorics

Quiver.Path.getElem_vertices_zero

∀ {V : Type u_1} [inst : Quiver V] {a b : V} (p : Quiver.Path a b), p.vertices[0] = a
Defined in
Mathlib.Combinatorics.Quiver.Path.Vertices
Cited by
2 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Quiver
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Quiver.Path.exists_eq_comp_and_length_eq_of_lt_length · cited by 1Path.exists_eq_comp_and_l…Quiver.Path.vertices_comp_get_length_eq · cited by 0Path.vertices_comp_get_le…Quiver.Hom · cited by 32603Quiver.HomQuiver · cited by 405QuiverQuiver.Path · cited by 166Quiver.PathQuiver.Path.length · cited by 39Path.lengthQuiver.Path.vertices · cited by 21Path.verticesQuiver.Path.vertices_length · cited by 5Path.vertices_lengthPath.getElem_vertices_zeroCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.