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Theorems · Theorem · commutative algebra

EuclideanDomain.mul_left_not_lt

∀ {R : Type u} [self : EuclideanDomain R] (a : R) {b : R}, b ≠ 0 → ¬EuclideanDomain.r (a * b) a

An additional constraint on r.

Defined in
Mathlib.Algebra.EuclideanDomain.Defs
Cited by
3 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
EuclideanDomain
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Around this declaration

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

EuclideanDomain.mul_right_not_lt · cited by 0EuclideanDomain.mul_right…EuclideanDomain.val_dvd_le · cited by 0EuclideanDomain.val_dvd_leEuclideanDomain.lt_one · cited by 0EuclideanDomain.lt_oneAddMonoid.toZero · cited by 325AddMonoid.toZeroEuclideanDomain · cited by 124EuclideanDomainEuclideanDomain.r · cited by 13EuclideanDomain.rEuclideanDomain.mul_left_not_…CITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.