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Theorems · Theorem · commutative algebra

zero_ne_one

∀ {α : Type u_2} [inst : Zero α] [inst_1 : One α] [NeZero 1], 0 ≠ 1
Defined in
Mathlib.Algebra.NeZero
Cited by
90 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
ZeroOneNeZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

not_isUnit_zero · cited by 20not_isUnit_zeroclosure_ball · cited by 20closure_ballComplex.I_ne_zero · cited by 19Complex.I_ne_zeroComplex.exp_ne_zero · cited by 19Complex.exp_ne_zeronontrivial_of_invariantBasisNumber · cited by 18nontrivial_of_invariantBa…FiniteField.card · cited by 10FiniteField.cardzero_ne_one' · cited by 10zero_ne_one'Invertible.ne_zero · cited by 10Invertible.ne_zeroIsFractionRing.isFractionRing_of_isDomain_of_isLocalization · cited by 6IsFractionRing.isFraction…Polynomial.induction_with_natDegree_le · cited by 4Polynomial.induction_with…multiplicity_eq_zero · cited by 3multiplicity_eq_zeroMatrix.det_mvPolynomialX_ne_zero · cited by 3Matrix.det_mvPolynomialX_…Polynomial.finiteMultiplicity_of_degree_pos_of_monic · cited by 3Polynomial.finiteMultipli…RingHom.map_one_ne_zero · cited by 3RingHom.map_one_ne_zeroConvex.finsum_mem · cited by 3Convex.finsum_memzero_ne_oneCITED BYCITES

Cites0

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Nothing in Mathlib beyond the foundations.

Cited by90

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