Theorems · Theorem · group theory
zero_ne_one_or_forall_eq_0
∀ {M₀ : Type u_1} [inst : MulZeroOneClass M₀], 0 ≠ 1 ∨ ∀ (a : M₀), a = 0In a monoid with zero, either zero and one are nonequal, or zero is the only element.
- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulZeroOneClass
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroOneClassstatement and proof · cited by 184
- not_or_of_impproof · cited by 8
- eq_zero_of_zero_eq_oneproof · cited by 2
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