Theorems · Theorem · group theory
iterate_map_zero
∀ {M : Type u_10} {F : Type u_11} [inst : Zero M] [inst_1 : FunLike F M M] [ZeroHomClass F M M] (f : F) (n : ℕ),
(⇑f)^[n] 0 = 0- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- ZeroFunLikeZeroHomClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- map_zeroproof · cited by 1,614
- Nat.iteratestatement · cited by 740
- ZeroHomClassstatement and proof · cited by 74
- Function.iterate_fixedproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- SkewPolynomial.X_mulproof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0proof · cited by 2
- bernsteinPolynomial.linearIndependent_auxproof · cited by 1
- Polynomial.iterate_derivative_zeroproof · cited by 1
- LinearMap.tendsto_birkhoffAverage_of_ker_subset_closureproof · cited by 1
- JacobsonNoether.exist_pow_eq_zero_of_leproof · cited by 1
- SkewPolynomial.X_pow_mulproof · cited by 1
- Polynomial.iterate_derivative_eq_zero_of_degree_ltproof · cited by 1
- SkewPolynomial.X_pow_mul_monomialproof · cited by 0