Theorems · Theorem · field theory
Polynomial.smeval_C
∀ {R : Type u_1} [inst : Semiring R] (r : R) {S : Type u_2} [inst_1 : AddCommMonoid S] [inst_2 : Pow S ℕ]
[inst_3 : MulActionWithZero R S] (x : S), (Polynomial.C r).smeval x = r • x ^ 0- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Polynomial.Cstatement and proof · cited by 1,598
- zero_smulproof · cited by 716
- MulActionWithZerostatement and proof · cited by 79
- Polynomial.smevalstatement · cited by 65
- Polynomial.smeval_eq_sumproof · cited by 9
- Polynomial.sum_C_indexproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.smeval_oneproof · cited by 10
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- Ring.smeval_ascPochhammer_succ_negproof · cited by 2
- Ring.descPochhammer_succ_succ_smevalproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1
- Polynomial.smeval_at_zeroproof · cited by 0