Theorems · Theorem · commutative algebra
gcd_eq_of_dvd_sub_right
∀ {α : Type u_1} [inst : CommRing α] [inst_1 : NormalizedGCDMonoid α] {a b c : α}, a ∣ b - c → gcd a b = gcd a c- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNormalizedGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- mul_assocproof · cited by 1,667
- add_commproof · cited by 1,535
- mul_addproof · cited by 413
- mul_subproof · cited by 201
- add_sub_cancel_rightproof · cited by 187
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdstatement and proof · cited by 143
- sub_sub_cancelproof · cited by 105
- add_sub_assocproof · cited by 72
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- Finset.gcd_eq_of_dvd_subproof · cited by 1
- gcd_eq_of_dvd_sub_leftproof · cited by 0