Theorems · Theorem · commutative algebra
dvd_antisymm_of_normalize_eq
∀ {α : Type u_1} [inst : MonoidWithZero α] [inst_1 : NormalizationMonoid α] [IsLeftCancelMulZero α] {a b : α},
normalize a = a → normalize b = b → a ∣ b → b ∣ a → a = b- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MonoidWithZerostatement and proof · cited by 456
- NormalizationMonoidstatement and proof · cited by 165
- normalizestatement and proof · cited by 137
- IsLeftCancelMulZerostatement and proof · cited by 48
- normalize_eq_normalizeproof · cited by 5
Cited by15
Results whose statement or proof uses this declaration.
- gcd_commproof · cited by 6
- gcd_one_rightproof · cited by 5
- gcd_assocproof · cited by 3
- Polynomial.content_eq_gcd_range_of_ltproof · cited by 2
- gcd_one_leftproof · cited by 2
- Associated.gcd_eq_leftproof · cited by 2
- Associated.gcd_eq_rightproof · cited by 2
- lcm_assocproof · cited by 2
- lcm_commproof · cited by 2
- gcd_eq_of_dvd_sub_rightproof · cited by 2
- lcm_eq_of_associated_leftproof · cited by 1
- gcd_eq_left_iffproof · cited by 1