Theorems · Theorem · group theory
left_ne_zero_of_mul_eq_one
∀ {M₀ : Type u_1} [inst : MulZeroOneClass M₀] [Nontrivial M₀] {a b : M₀}, a * b = 1 → a ≠ 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MulZeroOneClassNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- MulZeroOneClassstatement and proof · cited by 184
- left_ne_zero_of_mulproof · cited by 27
- ne_zero_of_eq_oneproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Units.ne_zeroproof · cited by 68
- Polynomial.natDegree_eq_zero_of_isUnitproof · cited by 5
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- ENNReal.eq_inv_of_mul_eq_one_leftproof · cited by 3
- Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zeroproof · cited by 1
- HahnSeries.isUnit_iffproof · cited by 0