Theorems · Theorem · commutative algebra
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 + c- Defined in
- Mathlib.Algebra.Ring.Divisibility.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- AddSemigroupLeftDistribClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semigroupstatement and proof · cited by 202
- Dvd.introproof · cited by 26
- left_distribproof · cited by 19
- LeftDistribClassstatement and proof · cited by 12
- Dvd.elimproof · cited by 4
Cited by25
Results whose statement or proof uses this declaration.
- dvd_add_leftproof · cited by 7
- IsCoprime.mul_dvdproof · cited by 5
- IsRelPrime.of_add_mul_left_leftproof · cited by 5
- Multiset.dvd_sumproof · cited by 4
- Dvd.dvd.addproof · cited by 4
- IsCoprime.dvd_of_dvd_mul_rightproof · cited by 4
- emultiplicity_add_of_gtproof · cited by 3
- IsCoprime.dvd_of_dvd_mul_leftproof · cited by 3
- PadicInt.zmod_congr_of_sub_mem_span_auxproof · cited by 2
- exists_eq_pow_of_mul_eq_pow_of_coprimeproof · cited by 1
- divRadical_dvd_derivativeproof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1