Theorems · Inductive type · group theory
AddDistribAddAction
(M : Type u_9) → (N : Type u_10) → [AddMonoid M] → [AddMonoid N] → Type (max u_10 u_9)
Typeclass for additive actions on additive structures.
The key axiom here is vadd_add : g +ᵥ (x + y) = (g +ᵥ x) + (g +ᵥ y).
If G is an additive group with additive automorphism group Γ, then there is a natural instance
of AddDistribAddAction Γ G.
- Defined in
- Mathlib.Algebra.Group.Action.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement · cited by 2,864
Cited by11
Results whose statement or proof uses this declaration.
- AddDistribAddAction.extstatement and proof · cited by 1
- AddDistribAddAction.vadd_addstatement and proof · cited by 1
- vadd_add'statement and proof · cited by 0
- AddDistribAddAction.mk.noConfusionstatement · cited by 0
- AddDistribAddAction.casesOnstatement and proof · cited by 0
- AddDistribAddAction.ctorIdxstatement and proof · cited by 0
- AddDistribAddAction.ext_iffstatement and proof · cited by 0
- AddDistribAddAction.noConfusionstatement and proof · cited by 0
- AddDistribAddAction.noConfusionTypestatement and proof · cited by 0
- AddDistribAddAction.recOnstatement and proof · cited by 0
- AddDistribAddAction.vadd_zerostatement and proof · cited by 0