Theorems · Definition · group theory
uniqueOfZeroEqOne
{M₀ : Type u_1} → [inst : MulZeroOneClass M₀] → 0 = 1 → Unique M₀In a monoid with zero, if zero equals one, then zero is the unique element.
Somewhat arbitrarily, we define the default element to be 0.
All other elements will be provably equal to it, but not necessarily definitionally equal.
- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- MulZeroOneClass
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.
- Uniquestatement · cited by 400
- MulZeroOneClassstatement and proof · cited by 184
- eq_zero_of_zero_eq_oneproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.uniqueOfZeroMemproof · cited by 1