Projectivization.mk_eq_mk_iff_crossProduct_eq_zero
∀ {F : Type u_1} [inst : Field F] {v w : Fin 3 → F} (hv : v ≠ 0) (hw : w ≠ 0),
Projectivization.mk F v hv = Projectivization.mk F w hw ↔ (crossProduct v) w = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- not_iff_notproof · cited by 159
- Projectivizationstatement · cited by 111
- neg_ne_zeroproof · cited by 70
- Projectivization.mkstatement · cited by 55
- crossProductstatement and proof · cited by 27
- cross_anticommproof · cited by 5
- LinearIndependent.pair_iff'proof · cited by 4
- Projectivization.mk_eq_mk_iff'proof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Projectivization.cross_mk_of_nestatement and proof · cited by 2
- Projectivization.cross_orthogonal_leftproof · cited by 2
- Projectivization.cross_commproof · cited by 1
- Projectivization.cross_selfproof · cited by 0
- Configuration.ofField.eq_or_eq_of_orthogonalproof · cited by 0