sections_add — Mathlib

English

Sections distributes over addition: Sections(s+t) equals Sections(s) bound with Sections(t) augmented by element-wise addition.

Русский

Разделы распространяются на сумму: Sections(s+t) равны Sections(s) связей с Sections(t) дополненными суммой элементов.

LaTeX

$$$$ \\operatorname{Sections}(s+t) = \\operatorname{Sections}(s).\\operatorname{bind}(\\lambda m. \\operatorname{Sections}(t).\\operatorname{map}(m + \\cdot)). $$$$

Lean4

@[simp]
theorem sections_add (s t : Multiset (Multiset α)) :
    Sections (s + t) = (Sections s).bind fun m => (Sections t).map (m + ·) :=
  Multiset.induction_on s (by simp) fun a s ih => by simp [ih, bind_assoc, map_bind, bind_map]

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