Theorems · Theorem · group theory
LeftCancelMonoid.mul_eq_one
∀ {α : Type u} [inst : LeftCancelMonoid α] [Subsingleton αˣ] {a b : α}, a * b = 1 ↔ a = 1 ∧ b = 1- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- LeftCancelMonoidSubsingleton
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
- LeftCancelMonoidstatement and proof · cited by 28
- LeftCancelMonoid.eq_one_of_mul_rightproof · cited by 3
- LeftCancelMonoid.eq_one_of_mul_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- mul_eq_one'proof · cited by 0