image_mulSingle_Ioc — Mathlib

English

Let i ∈ ι and a, b ∈ α_i. The image of Ioc(a, b) under Pi.mulSingle i is the interval Ioc between Pi.mulSingle i a and Pi.mulSingle i b.

Русский

Пусть i ∈ ι и a, b ∈ α_i. Образ Ioc(a, b) под Pi.mulSingle i есть Ioc( Pi.mulSingle i a, Pi.mulSingle i b ).

LaTeX

$$$ \\mathrm{image}(\\Pi.mulSingle\, i)( \\mathrm{Ioc}(a,b) ) = \\mathrm{Ioc}( \\Pi.mulSingle i\, a, \\Pi.mulSingle i\, b ) $$$

Lean4

@[to_additive]
theorem image_mulSingle_Ioc (i : ι) (a b : α i) :
    Pi.mulSingle i '' Ioc a b = Ioc (Pi.mulSingle i a) (Pi.mulSingle i b) :=
  image_update_Ioc _ _ _ _

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