Theorems · Theorem · commutative algebra
AddSubmonoid.iSup_mul
∀ {R : Type u_2} [inst : NonUnitalNonAssocSemiring R] {ι : Sort u_4} (S : ι → AddSubmonoid R) (T : AddSubmonoid R),
(⨆ i, S i) * T = ⨆ i, S i * T- 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
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- MulZeroClass.zero_mulproof · cited by 1,625
- AddSubmonoidstatement and proof · cited by 1,178
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- AddMemClass.add_memproof · cited by 229
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- ZeroMemClass.zero_memproof · cited by 162
- right_distribproof · cited by 26
- AddSubmonoid.mulstatement · cited by 18
- AddSubmonoid.mem_iSup_of_memproof · cited by 6
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