Theorems · Theorem · commutative algebra
dvd_add_right
∀ {α : Type u_1} [inst : NonUnitalRing α] {a b c : α}, a ∣ b → (a ∣ b + c ↔ a ∣ c)If an element a divides another element b in a ring, a divides the sum of b and another
element c iff a divides c.
- Defined in
- Mathlib.Algebra.Ring.Divisibility.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- NonUnitalRing
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.
- add_commproof · cited by 1,535
- NonUnitalRingstatement and proof · cited by 422
- dvd_add_leftproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- emultiplicity_add_of_gtproof · cited by 3
- dvd_iff_dvd_of_dvd_subproof · cited by 3
- EuclideanDomain.dvd_mod_iffproof · cited by 2
- dvd_sub_rightproof · cited by 1
- dvd_add_self_leftproof · cited by 0