Theorems · Theorem · group theory

Submonoid.mem_pi

∀ {ι : Type u_4} {M : ι → Type u_5} [inst : (i : ι) → MulOneClass (M i)] (I : Set ι) {S : (i : ι) → Submonoid (M i)}
  {p : (i : ι) → M i}, p ∈ Submonoid.pi I S ↔ ∀ i ∈ I, p i ∈ S i

Defined in: Mathlib.Algebra.Group.Submonoid.Operations
Cited by: 0 results in Mathlib
Foundations: Depth 15 from the axioms · uses Quot.sound
Assumes: MulOneClass

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Setstatement and proof · cited by 53,352
Submonoidstatement and proof · cited by 3,086
MulOneClassstatement and proof · cited by 1,018
Submonoid.pistatement · cited by 17

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