Theorems · Theorem · difference equations
fwdDiff_iter_pow_eq_zero_of_lt
∀ {R : Type u_3} [inst : CommRing R] {j n : ℕ}, j < n → ((fwdDiff 1)^[n] fun r => r ^ j) = 0The n-th forward difference of the function x ↦ x^j is zero if j < n.
- Defined in
- Mathlib.Algebra.Group.ForwardDiff
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- Finset.rangeproof · cited by 1,341
- Nat.iteratestatement and proof · cited by 740
- one_powproof · cited by 521
- Nat.chooseproof · cited by 494
- nsmul_eq_mulproof · cited by 369
- Finset.sum_applyproof · cited by 234
Cited by3
Results whose statement or proof uses this declaration.
- fwdDiff_iter_eq_factorialproof · cited by 1
- Polynomial.fwdDiff_iter_degree_eq_factorialproof · cited by 1
- fwdDiff_iter_sum_mul_pow_eq_zeroproof · cited by 0