Theorems · Theorem · group theory
SubmonoidClass.mk_pow
∀ {M : Type u_5} [inst : Monoid M] {A : Type u_4} [inst_1 : SetLike A M] [inst_2 : SubmonoidClass A M] {S : A} (x : M)
(hx : x ∈ S) (n : ℕ), ⟨x, hx⟩ ^ n = ⟨x ^ n, ⋯⟩- Defined in
- Mathlib.Algebra.Group.Submonoid.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- MonoidSetLikeSubmonoidClass
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.
- Monoidstatement and proof · cited by 3,887
- SetLikestatement and proof · cited by 1,084
- SubmonoidClassstatement and proof · cited by 60
- pow_memstatement · cited by 46
Cited by2
Results whose statement or proof uses this declaration.
- Submonoid.pow_exponent_eq_oneproof · cited by 1
- Ideal.IsPrincipal.of_isPrincipal_pow_of_coprimeproof · cited by 0