finset_inf_factors — Mathlib

English

Membership arrow: mem of (insert b s) a equals (a=b) or mem of s a.

Русский

Членство: mem вставки b в s для a равно (a=b) или члена s a.

LaTeX

$$$ \\operatorname{mem}(\\mathrm{insert}\\ b\\ s\\, a) = \\operatorname{Or}(a=b, \\operatorname{mem}(s,a)) $$$

Lean4

@[simp]
theorem finset_inf_factors {I : Type*} {A B : C} {s : Finset I} {P : I → Subobject B} (f : A ⟶ B) :
    (s.inf P).Factors f ↔ ∀ i ∈ s, (P i).Factors f := by
  classical
    induction s using Finset.induction_on with
  | empty => simp [top_factors]
  | insert _ _ _ ih =>
    simp [ih]
      -- `i` is explicit here because often we'd like to defer a proof of `m`

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