Theorems · Theorem · field theory
Polynomial.map_one
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (f : R →+* S), Polynomial.map f 1 = 1- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 104 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.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- RingHom.compproof · cited by 899
- Polynomial.mapstatement · cited by 806
- Polynomial.eval₂_oneproof · cited by 20
Cited by38
Results whose statement or proof uses this declaration.
- Polynomial.mapRingHomproof · cited by 98
- Polynomial.map_cyclotomic_intproof · cited by 21
- Polynomial.Splits.mapproof · cited by 19
- Polynomial.Separable.mapproof · cited by 14
- Polynomial.prod_cyclotomic_eq_X_pow_sub_oneproof · cited by 11
- Polynomial.cyclotomic_oneproof · cited by 7
- ascPochhammer_mapproof · cited by 5
- descPochhammer_eval_eq_ascPochhammerproof · cited by 4
- descPochhammer_mapproof · cited by 3
- Polynomial.int_coeff_of_cyclotomic'proof · cited by 3
- Polynomial.int_cyclotomic_specproof · cited by 3