Theorems · Theorem · commutative algebra
IsCoprime.abs_left_iff
∀ {R : Type u} [inst : CommRing R] [inst_1 : LinearOrder R] [AddLeftMono R] (x y : R), IsCoprime |x| y ↔ IsCoprime x y- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LinearOrderstatement and proof · cited by 8,572
- absstatement · cited by 1,814
- AddLeftMonostatement and proof · cited by 687
- IsCoprimestatement and proof · cited by 321
- abs_of_nonnegproof · cited by 279
- le_or_gtproof · cited by 269
- abs_of_negproof · cited by 39
- IsCoprime.neg_left_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- IsCoprime.abs_right_iffproof · cited by 2
- IsCoprime.abs_leftproof · cited by 1
- IsCoprime.abs_abs_iffproof · cited by 0