residueClass_apply_zero — Mathlib

English

The abscissa of absolute convergence of residueClass is at most 1: abscissaOfAbsConv(residueClass a) ≤ 1.

Русский

Абсцисса абсолютной сходимости residueClass не превосходит 1: abscissaOfAbsConv(residueClass a) ≤ 1.

LaTeX

$$abscissaOfAbsConv(residueClass a) ≤ 1$$

Lean4

@[simp]
theorem residueClass_apply_zero : residueClass a 0 = 0 := by
  simp only [Set.indicator_apply_eq_zero, Set.mem_setOf_eq, Nat.cast_zero, map_zero, implies_true]

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