Theorems · Theorem · commutative algebra
AddSubmonoid.mul_mem_mul
∀ {R : Type u_2} [inst : NonUnitalNonAssocSemiring R] {M N : AddSubmonoid R} {m n : R}, m ∈ M → n ∈ N → m * n ∈ M * N- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubmonoidstatement and proof · cited by 1,178
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- AddSubmonoid.mulstatement · cited by 18
- AddSubmonoid.smul_mem_smulproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- AddSubmonoid.mul_comm_of_commuteproof · cited by 1
- AddSubmonoid.closure_mul_closureproof · cited by 1
- AddSubmonoid.iSup_mulproof · cited by 0
- AddSubmonoid.sup_mulproof · cited by 0