Theorems · Theorem · group theory
Submonoid.pow_exponent_eq_one
∀ {G : Type u} [inst : Monoid G] {S : Submonoid G} {g : G}, g ∈ S → g ^ Monoid.exponent ↥S = 1- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Submonoidstatement and proof · cited by 3,086
- Monoid.exponentstatement and proof · cited by 128
- Monoid.pow_exponent_eq_oneproof · cited by 13
- OneMemClass.coe_eq_oneproof · cited by 6
- SubmonoidClass.mk_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.pow_exponent_eq_oneproof · cited by 0