Theorems · Theorem · number theory
IsUltrametricDist.norm_fwdDiff_iter_apply_le
∀ {M : Type u_1} {G : Type u_2} [inst : TopologicalSpace M] [inst_1 : CompactSpace M] [inst_2 : AddCommMonoid M]
[inst_3 : SeminormedAddCommGroup G] [IsUltrametricDist G] (h : M) (f : C(M, G)) (m : M) (n : ℕ),
‖(fwdDiff h)^[n] (⇑f) m‖ ≤ ‖f‖Bound for iterated forward differences of a continuous function from a compact space to a nonarchimedean seminormed group.
- Defined in
- Mathlib.NumberTheory.Padics.MahlerBasis
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- AddCommMonoidstatement and proof · cited by 12,281
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousMapstatement and proof · cited by 2,491
- Finset.rangeproof · cited by 1,341
- Nat.iteratestatement · cited by 740
- norm_nonnegproof · cited by 725
- CompactSpacestatement and proof · cited by 593
Cited by1
Results whose statement or proof uses this declaration.
- PadicInt.fwdDiff_iter_le_of_forall_leproof · cited by 1