Theorems · Theorem · field theory
Polynomial.map_injective
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S),
Function.Injective ⇑f → Function.Injective (Polynomial.map f)- Defined in
- Mathlib.Algebra.Polynomial.Eval.Coeff
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffproof · cited by 1,045
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.extproof · cited by 118
- Polynomial.coeff_mapproof · cited by 114
Cited by27
Results whose statement or proof uses this declaration.
- Polynomial.prod_cyclotomic_eq_X_pow_sub_oneproof · cited by 11
- Polynomial.map_dvd_mapproof · cited by 5
- Polynomial.map_eq_zero_iffproof · cited by 5
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- X_pow_sub_C_eq_prodproof · cited by 2
- Polynomial.IsPrimitive.mul_map_mem_lifts_iffproof · cited by 2
- LinearMap.polyCharpolyAux_basisIndepproof · cited by 2
- Polynomial.Monic.irreducible_iff_irreducible_map_fraction_mapproof · cited by 2
- IsStronglyTranscendental.of_mapproof · cited by 2
- Polynomial.IsPrimitive.dvd_of_fraction_map_dvd_fraction_mapproof · cited by 1
- Polynomial.eq_X_sub_C_of_separable_of_root_eqproof · cited by 1