Theorems · Theorem · field theory
RatFunc.denom_ne_zero
∀ {K : Type u} [inst : Field K] (x : RatFunc K), x.denom ≠ 0- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 130 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- RatFuncstatement and proof · cited by 301
- Polynomial.Monic.ne_zeroproof · cited by 63
- RatFunc.denomstatement · cited by 59
- RatFunc.monic_denomproof · cited by 1
Cited by20
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.intDegree_mulproof · cited by 3
- RatFunc.eq_C_of_minpolyX_coeff_eq_zeroproof · cited by 3
- RatFunc.num_denom_mulproof · cited by 2
- RatFunc.num_dvdproof · cited by 2
- RatFunc.minpolyX_aeval_Xproof · cited by 2
- RatFunc.num_denom_negproof · cited by 1
- RatFunc.num_inv_dvdproof · cited by 1
- RatFunc.num_mul_denom_add_denom_mul_num_ne_zeroproof · cited by 1
- RatFunc.denom_add_dvdproof · cited by 1
- RatFunc.intDegree_addproof · cited by 1