Projectivization.mk_eq_mk_iff
∀ (K : Type u_1) {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] (v w : V)
(hv : v ≠ 0) (hw : w ≠ 0), Projectivization.mk K v hv = Projectivization.mk K w hw ↔ ∃ a, a • w = v- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Unitsstatement · cited by 2,804
- DivisionRingstatement and proof · cited by 1,062
- Projectivizationstatement · cited by 111
- Projectivization.mkstatement · cited by 55
- Quotient.eq''proof · cited by 44
Cited by4
Results whose statement or proof uses this declaration.
- Projectivization.mk_eq_mk_iff'proof · cited by 3
- Projectivization.exists_smul_eq_mk_repproof · cited by 2
- Projectivization.linearIndependent_pair_iff_neproof · cited by 1
- Projectivization.submodule_injectiveproof · cited by 0