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Theorems · Theorem · group theory

Finset.neg_nonempty_iff

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Neg α] {s : Finset α}, (-s).Nonempty ↔ s.Nonempty
Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by
4 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqNeg
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Around this declaration

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

Finset.Nonempty.of_neg · cited by 2Nonempty.of_negFinset.Nonempty.zsmul · cited by 1Nonempty.zsmulFinset.nonneg_subConst · cited by 1Finset.nonneg_subConstFinset.Nonempty.neg · cited by 1Nonempty.negFinset · cited by 13712FinsetFinset.Nonempty · cited by 1001Finset.NonemptyFinset.neg · cited by 63Finset.negFinset.image_nonempty · cited by 12Finset.image_nonemptyFinset.neg_nonempty_iffCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.