Theorems · Theorem · commutative algebra
extract_gcd
∀ {α : Type u_2} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] (x y : α),
∃ x' y', x = gcd x y * x' ∧ y = gcd x y * y' ∧ IsUnit (gcd x' y')- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.zero_mulproof · cited by 1,625
- IsUnitstatement · cited by 1,602
- CommMonoidWithZerostatement and proof · cited by 913
- GCDMonoid.gcdstatement and proof · cited by 143
- GCDMonoidstatement and proof · cited by 96
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- isUnit_gcd_of_eq_mul_gcdproof · cited by 3
- gcd_eq_zero_iffproof · cited by 3
- gcd_one_left'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.surj_of_gcd_domainproof · cited by 0