Theorems · Theorem · group theory
not_isLeftRegular_zero_iff
∀ {R : Type u_1} [inst : MulZeroClass R], ¬IsLeftRegular 0 ↔ Nontrivial RIn a non-trivial MulZeroClass, the 0 element is not left-regular.
- Defined in
- Mathlib.Algebra.GroupWithZero.Regular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MulZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement · cited by 2,416
- MulZeroClassstatement and proof · cited by 232
- IsLeftRegularstatement and proof · cited by 97
- not_iff_commproof · cited by 32
- nontrivial_iffproof · cited by 12
- subsingleton_iffproof · cited by 10
- isLeftRegular_zero_iff_subsingletonproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- not_isLeftRegular_zeroproof · cited by 1