Theorems · Theorem · group theory
vsub_left_injective
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p : P), Function.Injective fun x => x -ᵥ pSubtracting the point p is an injective function.
- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement · cited by 817
- vsub_left_cancelproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- EuclideanGeometry.left_ne_right_of_oangle_ne_zeroproof · cited by 4
- dist_add_dist_eq_iffproof · cited by 4
- AffineIndependent.finrank_vectorSpan_image_finsetproof · cited by 3
- affineIndependent_set_iff_linearIndependent_vsubproof · cited by 3
- linearIndependent_set_iff_affineIndependent_vadd_union_singletonproof · cited by 2
- sbtw_vsub_const_iffproof · cited by 2
- mem_vsub_const_affineSegmentproof · cited by 1
- finrank_vectorSpan_image_finset_leproof · cited by 1