Theorems · Theorem · commutative algebra
Submodule.pow_subset_pow
∀ {R : Type u} [inst : Semiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Module R A]
[inst_3 : IsScalarTower R A A] (M : Submodule R A) {n : ℕ}, ↑M ^ n ⊆ ↑(M ^ n)- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- IsScalarTowerstatement and proof · cited by 3,896
- transproof · cited by 111
- Set.NPowstatement · cited by 51
- Submodule.le_pow_toAddSubmonoidproof · cited by 1
- AddSubmonoid.pow_subset_powproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.pow_mem_powproof · cited by 3
- ExteriorAlgebra.ιMulti_rangeproof · cited by 2