Theorems · Theorem · field theory
Polynomial.eval_C_mul
∀ {R : Type u} {a : R} [inst : Semiring R] {p : Polynomial R} {x : R},
Polynomial.eval x (Polynomial.C a * p) = a * Polynomial.eval x p- Defined in
- Mathlib.Algebra.Polynomial.Eval.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_assocproof · cited by 1,667
- Polynomial.Cstatement and proof · cited by 1,598
- Polynomial.evalstatement and proof · cited by 796
- mul_addproof · cited by 413
- Polynomial.eval_addproof · cited by 84
- Polynomial.induction_on'proof · cited by 50
- Polynomial.eval_monomialproof · cited by 21
- Polynomial.C_mul_monomialproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- descPochhammer_succ_evalproof · cited by 3
- ascPochhammer_succ_evalproof · cited by 3
- Polynomial.eval_natCast_mulproof · cited by 2
- Polynomial.IsUnitTrinomial.irreducible_aux3proof · cited by 1