Theorems · Theorem · group theory
LeftCancelMonoid.mul_ne_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 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoidSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- not_iff_commproof · cited by 32
- LeftCancelMonoidstatement and proof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- mul_ne_one'proof · cited by 0