Theorems · Theorem · commutative algebra
EuclideanDomain.GCD.induction
∀ {R : Type u} [inst : EuclideanDomain R] {P : R → R → Prop} (a b : R),
(∀ (x : R), P 0 x) → (∀ (a b : R), a ≠ 0 → P (b % a) a → P a b) → P a b- Defined in
- Mathlib.Algebra.EuclideanDomain.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- EuclideanDomainstatement and proof · cited by 124
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_dvdproof · cited by 8
- Polynomial.gcd_mapproof · cited by 2
- EuclideanDomain.dvd_gcdproof · cited by 1
- EuclideanDomain.xgcdAux_Pproof · cited by 1
- EuclideanDomain.xgcdAux_fstproof · cited by 1