Theorems · Theorem · commutative algebra
dvd_sub_left
∀ {α : Type u_1} [inst : NonUnitalRing α] {a b c : α}, a ∣ c → (a ∣ b - c ↔ a ∣ b)If an element a divides another element c in a ring, a divides the difference of another
element b with c iff a divides b.
- Defined in
- Mathlib.Algebra.Ring.Divisibility.Basic
- Cited by
- 1 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.
- NonUnitalRingstatement and proof · cited by 422
- dvd_negproof · cited by 19
- dvd_add_leftproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- dvd_sub_self_rightproof · cited by 0