Theorems · Theorem · group theory
Submonoid.pow_smul_mem_closure_smul
∀ {M : Type u_3} [inst : Monoid M] {N : Type u_7} [inst_1 : CommMonoid N] [inst_2 : MulAction M N] [IsScalarTower M N N]
(r : M) (s : Set N) {x : N}, x ∈ Submonoid.closure s → ∃ n, r ^ n • x ∈ Submonoid.closure (r • s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- IsScalarTowerstatement and proof · cited by 3,896
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- mul_commproof · cited by 2,262
- one_smulproof · cited by 1,374
- MulActionstatement and proof · cited by 1,294
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- Set.smulSetstatement · cited by 608
- pow_addproof · cited by 315
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.pow_smul_mem_of_smul_subset_of_mem_adjoinproof · cited by 2