Theorems · Theorem · group theory
add_vadd_comm
∀ {α : Type u_5} {β : Type u_6} [inst : Add β] [inst_1 : VAdd α β] [VAddCommClass α β β] (s : α) (x y : β),
x + (s +ᵥ y) = s +ᵥ x + y- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddVAddVAddCommClass
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.
- HVAdd.hVAddstatement · cited by 1,820
- VAddstatement and proof · cited by 616
- VAddCommClassstatement and proof · cited by 41
- VAddCommClass.vadd_commproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- add_ballproof · cited by 4
- IsCompact.add_closedBallproof · cited by 3
- AddSemiconjBy.vadd_leftproof · cited by 2
- AddSemiconjBy.vadd_rightproof · cited by 2
- Finset.addDysonETransform.subsetproof · cited by 0
- AddAction.stabilizer_image_coe_quotientproof · cited by 0