Theorems · Theorem · commutative algebra

Dvd.dvd.of_neg_left

∀ {α : Type u_1} [inst : Semigroup α] [inst_1 : HasDistribNeg α] {a b : α}, -a ∣ b → a ∣ b

Alias of the forward direction of neg_dvd. The negation of an element a of a semigroup with a distributive negation divides another element b iff a divides b.

Defined in: Mathlib.Algebra.Ring.Divisibility.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Quot.sound
Assumes: Semigroup HasDistribNeg

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Semigroupstatement and proof · cited by 202
HasDistribNegstatement and proof · cited by 114
neg_dvdproof · cited by 3

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