Theorems · Theorem · complex analysis
Complex.re_le_norm
∀ (z : ℂ), z.re ≤ ‖z‖
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- Complex.restatement · cited by 882
- abs_leproof · cited by 64
- Complex.abs_re_le_normproof · cited by 9
Cited by5
Results whose statement or proof uses this declaration.
- mellin_hasDerivAt_of_isBigO_rpowproof · cited by 2
- PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decayproof · cited by 1
- Complex.ball_one_subset_slitPlaneproof · cited by 1
- Complex.IsExpCmpFilter.isLittleO_log_norm_reproof · cited by 1
- Complex.norm_add_le'proof · cited by 0