Theorems · Theorem · complex analysis
Complex.UnitClosedDisc.norm_le_one
∀ (z : Complex.UnitClosedDisc), ‖↑z‖ ≤ 1
- Defined in
- Mathlib.Analysis.Complex.UnitDisc.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 140 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 · cited by 5,565
- Norm.normstatement · cited by 5,413
- Complex.UnitClosedDiscstatement and proof · cited by 42
- Complex.UnitClosedDisc.coestatement · cited by 26
- mem_closedBall_zero_iffproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- Complex.UnitClosedDisc.casesOnproof · cited by 1
- Complex.UnitClosedDisc.sq_norm_lt_oneproof · cited by 1
- Complex.UnitClosedDisc.existsproof · cited by 0
- Complex.UnitClosedDisc.mk_coestatement · cited by 0
- Complex.UnitClosedDisc.forallproof · cited by 0