Theorems · Theorem
Matrix.range_empty
∀ {α : Type u} (u : Fin 0 → α), Set.range u = ∅- Defined in
- Mathlib.Data.Fin.VecNotation
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- Set.range_eq_emptyproof · cited by 14
Cited by14
Results whose statement or proof uses this declaration.
- affineIndependent_iff_not_collinear_setproof · cited by 7
- finrank_eq_one_iff_of_nonzeroproof · cited by 3
- RootPairing.Base.linearIndependent_pair_of_neproof · cited by 2
- RootPairing.EmbeddedG2.mem_span_of_mem_allRootsproof · cited by 1
- Matrix.range_cons_emptyproof · cited by 1
- NumberField.exists_nat_le_mulHeight₁proof · cited by 1
- Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparableproof · cited by 1
- ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDerivproof · cited by 1
- EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_neproof · cited by 1
- EuclideanGeometry.cospherical_of_mul_dist_eq_mul_dist_of_angle_eq_piproof · cited by 0
- Projectivization.linearIndepOn_pairproof · cited by 0