Theorems · Theorem · field theory
RatFunc.num_div_denom
∀ {K : Type u} [inst : Field K] (x : RatFunc K),
(algebraMap (Polynomial K) (RatFunc K)) x.num / (algebraMap (Polynomial K) (RatFunc K)) x.denom = x- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_commproof · cited by 2,262
- Polynomial.Cproof · cited by 1,598
- map_mulproof · cited by 1,137
- Polynomial.leadingCoeffproof · cited by 498
- RatFuncstatement and proof · cited by 301
- GCDMonoid.gcdproof · cited by 143
- inv_ne_zeroproof · cited by 99
Cited by18
Results whose statement or proof uses this declaration.
- RatFunc.num_denom_addproof · cited by 3
- RatFunc.num_mul_eq_mul_denom_iffproof · cited by 3
- RatFunc.denom_dvdproof · cited by 3
- RatFunc.num_denom_mulproof · cited by 2
- RatFunc.num_dvdproof · cited by 2
- RatFunc.eq_C_iffproof · cited by 2
- RatFunc.minpolyX_aeval_Xproof · cited by 2
- RatFunc.liftMonoidWithZeroHom_applyproof · cited by 2
- RatFunc.num_denom_negproof · cited by 1
- RatFunc.num_eq_zero_iffproof · cited by 1
- RatFunc.num_inv_dvdproof · cited by 1
- RatFunc.denom_add_dvdproof · cited by 1