Theorems · Theorem · field theory
Polynomial.smeval_X
∀ (R : Type u_1) [inst : Semiring R] {S : Type u_2} [inst_1 : AddCommMonoid S] [inst_2 : Pow S ℕ]
[inst_3 : MulActionWithZero R S] (x : S), Polynomial.X.smeval x = x ^ 1- Defined in
- Mathlib.Algebra.Polynomial.Smeval
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- AddCommMonoidstatement and proof · cited by 12,281
- Polynomial.Xstatement and proof · cited by 1,639
- one_smulproof · cited by 1,374
- 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_X_indexproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- Ring.descPochhammer_eq_factorial_smul_chooseproof · cited by 8
- Complex.one_add_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- Polynomial.descPochhammer_smeval_eq_ascPochhammerproof · cited by 2
- Ring.multichoose_one_right'proof · cited by 2
- Ring.smeval_ascPochhammer_succ_negproof · cited by 2
- Polynomial.ascPochhammer_smeval_neg_eq_descPochhammerproof · cited by 1
- Polynomial.descPochhammer_smeval_eq_descFactorialproof · cited by 1
- Ring.descPochhammer_smeval_addproof · cited by 1
- Ring.descPochhammer_succ_succ_smevalproof · cited by 1
- Ring.ascPochhammer_succ_succproof · cited by 1
- Ring.choose_smul_chooseproof · cited by 1