Theorems · Theorem · commutative algebra
gcd_dvd_gcd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] {a b c d : α}, a ∣ b → c ∣ d → gcd a c ∣ gcd b d- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Dvd.dvd.transproof · cited by 148
- GCDMonoid.gcdstatement · cited by 143
- GCDMonoidstatement and proof · cited by 96
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- GCDMonoid.dvd_gcdproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- Associated.gcdproof · cited by 4
- Associated.gcd_eq_leftproof · cited by 2
- Associated.gcd_eq_rightproof · cited by 2
- pow_dvd_of_mul_eq_powproof · cited by 1
- gcd_dvd_gcd_mul_leftproof · cited by 0
- gcd_dvd_gcd_mul_left_rightproof · cited by 0
- gcd_dvd_gcd_mul_rightproof · cited by 0
- gcd_dvd_gcd_mul_right_rightproof · cited by 0