Theorems · Theorem · complex analysis
Complex.lim_norm
∀ (f : CauSeq ℂ fun x => ‖x‖), (Complex.cauSeqNorm f).lim = ‖f.lim‖
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- absstatement and proof · cited by 1,814
- lt_of_le_of_ltproof · cited by 432
- CauSeqstatement and proof · cited by 189
- CauSeq.constproof · cited by 58
- CauSeq.limstatement and proof · cited by 35
- CauSeq.equiv_limproof · cited by 15
- CauSeq.lim_eq_of_equiv_constproof · cited by 8
- abs_norm_sub_norm_leproof · cited by 7
- Complex.cauSeqNormstatement and proof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Complex.exp_boundproof · cited by 6
- Complex.norm_exp_sub_sum_le_exp_norm_sub_sumproof · cited by 1
- Complex.norm_exp_sub_sum_le_norm_mul_expproof · cited by 0
- Complex.exp_bound'proof · cited by 0