Theorems · Theorem · group theory
right_ne_zero_of_mul_eq_one
∀ {M₀ : Type u_1} [inst : MulZeroOneClass M₀] [Nontrivial M₀] {a b : M₀}, a * b = 1 → b ≠ 0- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 7 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
- right_ne_zero_of_mulproof · cited by 38
- ne_zero_of_eq_oneproof · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.Monic.eq_one_of_isUnitproof · cited by 6
- Polynomial.natDegree_eq_zero_of_isUnitproof · cited by 5
- ENNReal.eq_inv_of_mul_eq_one_leftproof · cited by 3
- Polynomial.not_isFieldproof · cited by 3
- Polynomial.not_isUnit_X_add_Cproof · cited by 0
- Lagrange.sum_nodalWeight_mul_inv_sub_ne_zeroproof · cited by 0
- HahnSeries.isUnit_iffproof · cited by 0