Theorems · Definition · group theory
Submonoid.pow
{M : Type u_1} → [inst : Monoid M] → (n : M) → ℕ → ↥(Submonoid.powers n)Exponentiation map from natural numbers to powers.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 25 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- Submonoid.powersstatement · cited by 408
- Multiplicative.ofAddproof · cited by 237
- powersHomproof · cited by 6
- MonoidHom.mrangeRestrictproof · cited by 5
Cited by15
Results whose statement or proof uses this declaration.
- selfZPowproof · cited by 14
- Submonoid.powLogEquivproof · cited by 4
- selfZPow_mul_negproof · cited by 3
- selfZPow_of_negstatement · cited by 2
- selfZPow_of_nonposstatement and proof · cited by 2
- Submonoid.pow_applystatement · cited by 2
- Submonoid.pow_coestatement and proof · cited by 1
- Submonoid.pow_log_eq_selfstatement · cited by 1
- Submonoid.pow_right_injective_iff_pow_injectivestatement and proof · cited by 1
- selfZPow_addproof · cited by 1
- selfZPow_neg_natCaststatement and proof · cited by 1
- selfZPow_sub_natCaststatement and proof · cited by 1