Theorems · Theorem · group theory
mul_eq_one
∀ {α : Type u} [inst : CommMonoid α] [Subsingleton αˣ] {a b : α}, a * b = 1 ↔ a = 1 ∧ b = 1- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- CommMonoidSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- eq_one_of_mul_leftproof · cited by 1
- eq_one_of_mul_rightproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- dvd_antisymmproof · cited by 23
- Zsqrtd.norm_eq_one_iffproof · cited by 3
- GaussianInt.sq_add_sq_of_nat_prime_of_not_irreducibleproof · cited by 2
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1
- Associates.exists_mem_multiset_le_of_primeproof · cited by 0
- Associates.eq_pow_of_mul_eq_powproof · cited by 0