Theorems · Theorem · commutative algebra
AddSubmonoid.sup_mul
∀ {R : Type u_2} [inst : NonUnitalNonAssocSemiring R] {M N P : AddSubmonoid R}, (M ⊔ N) * P = M * P ⊔ N * P- Defined in
- Mathlib.Algebra.Ring.Submonoid.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalNonAssocSemiring
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_antisymmproof · cited by 2,068
- AddSubmonoidstatement and proof · cited by 1,178
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- right_distribproof · cited by 26
- AddSubmonoid.mulstatement · cited by 18
- AddSubmonoid.mem_supproof · cited by 8
- AddSubmonoid.mul_leproof · cited by 5
- AddSubmonoid.mul_mem_mulproof · cited by 4
- AddSubmonoid.add_mem_supproof · cited by 3
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