Theorems · Theorem · complex analysis
Complex.canonicalFactor_eq_zero_iff
∀ {R : ℝ} {w z : ℂ}, w ∈ Metric.ball 0 R → z ∈ Metric.ball 0 R → (Complex.canonicalFactor R w z = 0 ↔ z = w)The function CanonicalFactor R w vanishes only at w.
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- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Metric.ballstatement and proof · cited by 735
- Metric.ball_subset_closedBallproof · cited by 46
- Complex.canonicalFactorstatement and proof · cited by 20
- Complex.canonicalFactor_ne_zeroproof · cited by 6
- Complex.canonicalFactor_apply_selfproof · cited by 2
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