Theorems · Theorem · group theory
SemigroupIdeal.coe_closure
∀ {M : Type u_1} [inst : Semigroup M] {s : Set M}, ↑(SemigroupIdeal.closure s) = s ∪ Set.univ * sThe semigroup ideal generated by s is s ∪ Set.univ * s.
- Defined in
- Mathlib.Algebra.Group.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- SetLike.coestatement and proof · cited by 8,199
- Set.univstatement and proof · cited by 3,945
- LE.le.antisymmproof · cited by 507
- Set.mem_univproof · cited by 416
- Set.mulstatement · cited by 297
- Semigroupstatement and proof · cited by 202
- Set.mul_mem_mulproof · cited by 22
- SemigroupIdealstatement and proof · cited by 12
- SemigroupIdeal.closurestatement and proof · cited by 11
- SemigroupIdeal.mem_closure_of_memproof · cited by 1
- SemigroupIdeal.mul_memproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- SemigroupIdeal.coe_closure'proof · cited by 1
- SemigroupIdeal.mem_closure'proof · cited by 0