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Theorems · Theorem · group theory

AddSubmonoid.mem_pi

∀ {ι : Type u_4} {M : ι → Type u_5} [inst : (i : ι) → AddZeroClass (M i)] (I : Set ι) {S : (i : ι) → AddSubmonoid (M i)}
  {p : (i : ι) → M i}, p ∈ AddSubmonoid.pi I S ↔ ∀ i ∈ I, p i ∈ S i
Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses Quot.sound
Assumes
AddZeroClass
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Around this declaration

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AddSubmonoid.pi_top · cited by 0AddSubmonoid.pi_topAddSubmonoid.pi_bot · cited by 0AddSubmonoid.pi_botAddSubmonoid.pi_empty · cited by 0AddSubmonoid.pi_emptySet · cited by 53352SetAddZeroClass · cited by 1237AddZeroClassAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.pi · cited by 20AddSubmonoid.piAddSubmonoid.mem_piCITED BYCITES

Cites4

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Cited by3

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