multiplicity_le_emultiplicity — Mathlib

English

multiplicity a b ≤ emultiplicity a b

Русский

кратность a b ≤ эмплипичность a b

LaTeX

$$$ multiplicity(a,b) \le emultiplicity(a,b) $$$

Lean4

@[simp]
theorem multiplicity_le_emultiplicity : multiplicity a b ≤ emultiplicity a b :=
  by
  by_cases hf : FiniteMultiplicity a b
  · simp [hf.emultiplicity_eq_multiplicity]
  ·
    simp [hf, emultiplicity_eq_top.2]
      -- Cannot be @[simp] because `β`, `c`, and `d` cannot be inferred by `simp`.

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