Theorems · Theorem · commutative algebra
Dvd.dvd.add
∀ {α : Type u_1} [inst : Add α] [inst_1 : Semigroup α] [LeftDistribClass α] {a b c : α}, a ∣ b → a ∣ c → a ∣ b + cAlias of dvd_add.
- Defined in
- Mathlib.Algebra.Ring.Divisibility.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- AddSemigroupLeftDistribClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semigroupstatement · cited by 202
- dvd_addproof · cited by 25
- LeftDistribClassstatement · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- dvd_subproof · cited by 9
- PadicInt.isCauSeq_padicNorm_of_pow_dvd_subproof · cited by 2
- Polynomial.pow_sub_one_dvd_derivative_of_pow_dvdproof · cited by 2
- min_pow_dvd_addproof · cited by 1