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Theorems · Theorem · group theory

Set.Nonempty.subset_zero_iff

∀ {α : Type u_2} [inst : Zero α] {s : Set α}, s.Nonempty → (s ⊆ 0 ↔ s = 0)
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Zero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.add_eq_zero_iff · cited by 1Filter.add_eq_zero_iffSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.zero · cited by 87Set.zeroSet.Nonempty.subset_singleton_iff · cited by 5Nonempty.subset_singleton…Nonempty.subset_zero_iffCITED BYCITES

Cites4

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Cited by1

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