Theorems · Theorem · combinatorics
Quiver.Path.eq_of_length_zero
∀ {V : Type u} [inst : Quiver V] {a b : V} (p : Quiver.Path a b), p.length = 0 → a = b- Defined in
- Mathlib.Combinatorics.Quiver.Path
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- Quiverstatement and proof · cited by 405
- Quiver.Pathstatement and proof · cited by 166
- Quiver.Path.lengthstatement and proof · cited by 39
- Quiver.Path.casesOnproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Quiver.Path.eq_toPath_comp_of_length_eq_succproof · cited by 2
- Quiver.Path.exists_notMem_mem_hom_path_path_of_notMem_memproof · cited by 1
- Matrix.pow_apply_pos_iff_nonempty_pathproof · cited by 1
- Quiver.eq_nil_of_length_zerostatement and proof · cited by 0
- Matrix.IsIrreducible.exists_posproof · cited by 0