Theorems · Theorem · group theory
eq_vadd_iff_vsub_eq
∀ {G : Type u_1} {P : Type u_2} [inst : AddGroup G] [T : AddTorsor G P] (p₁ : P) (g : G) (p₂ : P),
p₁ = g +ᵥ p₂ ↔ p₁ -ᵥ p₂ = gConvert between an equality with adding a group element to a point and an equality of a subtraction of two points with a group element.
- Defined in
- Mathlib.Algebra.Torsor.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by16
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_eq_pi_iff_sbtwproof · cited by 6
- collinear_iff_of_memproof · cited by 4
- Wbtw.trans_expand_leftproof · cited by 2
- Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_pointproof · cited by 2
- EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_mem_of_finrank_eq_twoproof · cited by 2
- AffineSubspace.wOppSide_self_iffproof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_distproof · cited by 1
- EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpointproof · cited by 1
- EuclideanGeometry.Sphere.secondInter_eq_self_iffproof · cited by 1
- Affine.Simplex.centroid_mem_medianproof · cited by 1
- EuclideanGeometry.reflection_eq_self_iffproof · cited by 1
- vadd_eq_vadd_iff_neg_add_eq_vsubproof · cited by 1