Theorems · Theorem · group theory
AddSemigroupIdeal.add_mem
∀ {M : Type u_1} [inst : Add M] (I : AddSemigroupIdeal M) (x : M) {y : M}, y ∈ I → x + y ∈ I- Defined in
- Mathlib.Algebra.Group.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSemigroupIdealstatement and proof · cited by 12
- SubAddAction.vadd_memproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddSemigroupIdeal.coe_closureproof · cited by 2