Theorems · Definition · group theory
Set.monoid
{α : Type u_2} → [Monoid α] → Monoid (Set α)Set α is a Monoid under pointwise operations if α is.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 26 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.
- Setstatement and proof · cited by 53,352
- Monoidstatement and proof · cited by 3,887
- MulOneClassproof · cited by 1,018
- Semigroupproof · cited by 202
- Set.NPowproof · cited by 51
- Set.mulOneClassproof · cited by 4
- Set.semigroupproof · cited by 0
Cited by28
Results whose statement or proof uses this declaration.
- Set.commMonoidproof · cited by 21
- IsApproximateSubgroup.sq_covBySMulstatement · cited by 6
- Set.pow_right_monotonestatement · cited by 3
- Set.pow_subset_pow_mul_of_sq_subset_mulstatement · cited by 2
- Set.Nonempty.powstatement · cited by 2
- IsUnit.setstatement · cited by 2
- coe_set_powstatement · cited by 1
- IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sqstatement · cited by 1
- Set.image_powstatement · cited by 1
- Set.image_pow_of_ne_zerostatement · cited by 1
- Set.pow_mul_subgroupClosurestatement · cited by 1
- Set.isUnit_singletonstatement · cited by 0