Theorems · Theorem · group theory
Set.mul_eq_one_iff
∀ {α : Type u_2} [inst : DivisionMonoid α] {s t : Set α}, s * t = 1 ↔ ∃ a b, s = {a} ∧ t = {b} ∧ a * b = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Nonemptyproof · cited by 2,627
- Set.mulstatement · cited by 297
- DivisionMonoidstatement and proof · cited by 201
- Eq.subsetproof · cited by 124
- Set.onestatement · cited by 54
- Set.mem_image2_of_memproof · cited by 40
- Set.eq_singleton_iff_unique_memproof · cited by 20
- inv_eq_of_mul_eq_one_rightproof · cited by 15
- eq_inv_of_mul_eq_one_leftproof · cited by 15
- Set.Nonempty.of_image2_leftproof · cited by 12
- Set.Nonempty.of_image2_rightproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- Filter.mul_eq_one_iffproof · cited by 1
- Set.isUnit_iffproof · cited by 0