Theorems · Theorem · group theory
Subsemigroup.mem_iSup
∀ {M : Type u_1} [inst : Mul M] {ι : Sort u_3} (p : ι → Subsemigroup M) {m : M},
m ∈ ⨆ i, p i ↔ ∀ (N : Subsemigroup M), (∀ (i : ι), p i ≤ N) → m ∈ N- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
Around this declaration
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Cites4
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
- Subsemigroupstatement and proof · cited by 323
- le_iSup_iffproof · cited by 16
- Subsemigroup.closure_singleton_le_iff_memproof · cited by 1
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