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Theorems · Theorem · group theory

Finset.mul_eq_one_iff

∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : DivisionMonoid α] {s t : Finset α},
  s * t = 1 ↔ ∃ a b, s = {a} ∧ t = {b} ∧ a * b = 1
Defined in
Mathlib.Algebra.Group.Pointwise.Finset.Basic
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DecidableEqDivisionMonoid
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Around this declaration

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

Finset.isUnit_iff · cited by 0Finset.isUnit_iffFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeDivisionMonoid · cited by 201DivisionMonoidFinset.mul · cited by 155Finset.mulFinset.coe_singleton · cited by 145Finset.coe_singletonFinset.one · cited by 43Finset.oneFinset.coe_mul · cited by 18Finset.coe_mulFinset.coe_one · cited by 4Finset.coe_oneFinset.mul_eq_one_iffCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.