Theorems · Theorem · commutative algebra
EuclideanDomain.xgcdAux_P
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] (a b : R) {r r' s t s' t' : R},
EuclideanDomain.P✝ a b (r, s, t) →
EuclideanDomain.P✝ a b (r', s', t') → EuclideanDomain.P✝ a b (EuclideanDomain.xgcdAux r s t r' s' t')- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomainDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- add_mulproof · cited by 363
- mul_subproof · cited by 201
- EuclideanDomainstatement and proof · cited by 124
- sub_subproof · cited by 54
- sub_add_eq_add_subproof · cited by 29
- add_subproof · cited by 21
- EuclideanDomain.xgcdAuxstatement and proof · cited by 7
- EuclideanDomain.GCD.inductionproof · cited by 5
- EuclideanDomain.xgcd_zero_leftproof · cited by 4
- EuclideanDomain.xgcdAux_recproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_eq_gcd_abproof · cited by 2