Theorems · Theorem · commutative algebra
AddSubmonoid.closure_mul_closure
∀ {R : Type u_2} [inst : NonUnitalNonAssocSemiring R] (S T : Set R),
AddSubmonoid.closure S * AddSubmonoid.closure T = AddSubmonoid.closure (S * T)- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- le_antisymmproof · cited by 2,068
- AddSubmonoidstatement · cited by 1,178
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Set.mulstatement · cited by 297
- AddSubmonoid.closurestatement and proof · cited by 224
- AddSubmonoid.subset_closureproof · cited by 63
- AddSubmonoid.closure_leproof · cited by 35
- Set.mul_mem_mulproof · cited by 22
- AddSubmonoid.mulstatement · cited by 18
- AddSubmonoid.mem_comapproof · cited by 8
- AddSubmonoid.mul_leproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.mul_eq_closure_mul_setproof · cited by 0