Theorems · Theorem · group theory
vadd_vadd
∀ {M : Type u_1} {α : Type u_5} [inst : AddMonoid M] [inst_1 : AddAction M α] (a₁ a₂ : M) (b : α),
a₁ +ᵥ a₂ +ᵥ b = (a₁ + a₂) +ᵥ b- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
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.
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddstatement · cited by 1,820
- AddActionstatement and proof · cited by 820
- AddSemigroupAction.add_vaddproof · cited by 43
Cited by40
Results whose statement or proof uses this declaration.
- neg_vadd_vaddproof · cited by 34
- vadd_neg_vaddproof · cited by 31
- AffineEquiv.pointReflection_midpoint_leftproof · cited by 5
- AddAction.isBlock_iff_disjoint_vadd_of_neproof · cited by 3
- AffineSubspace.shift_eqproof · cited by 3
- AffineSubspace.mem_affineSpan_insert_iffproof · cited by 3
- AddGroupFilterBasis.nhds_eqproof · cited by 3
- MeasureTheory.Measure.pairwise_aedisjoint_of_aedisjoint_forall_ne_zeroproof · cited by 2
- AddAction.isPretransitive_iff_baseproof · cited by 2
- MeasureTheory.measure_inter_neg_vaddproof · cited by 2
- Equiv.pointReflection_midpoint_leftproof · cited by 2
- AddAction.mem_orbit_of_mem_orbitproof · cited by 2