Theorems · Theorem · group theory
IsLeftRegular.ne_zero
∀ {R : Type u_1} [inst : MulZeroClass R] {a : R} [Nontrivial R], IsLeftRegular a → a ≠ 0A left-regular element of a Nontrivial MulZeroClass is non-zero.
- Defined in
- Mathlib.Algebra.GroupWithZero.Regular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses propext
- Assumes
- MulZeroClassNontrivial
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.
- Nontrivialstatement and proof · cited by 2,416
- MulZeroClass.zero_mulproof · cited by 1,625
- MulZeroClassstatement and proof · cited by 232
- IsLeftRegularstatement and proof · cited by 97
- exists_pair_neproof · cited by 32
Cited by1
Results whose statement or proof uses this declaration.
- IsRegular.ne_zeroproof · cited by 7