projIcc — Mathlib

English

Projection to the closed interval [a, b], computed as max(a, min(b, x)), with the natural bounds a ≤ value ≤ b.

Русский

Проекция на замкнутый интервал [a, b], равна max(a, min(b, x)) с несложными границами a ≤ значение ≤ b.

LaTeX

$$projIcc(a,b,h,x) = ⟨ max(a, min(b, x)), le_max_left(a, min(b,x)), max_le h (min_le_left _ _) ⟩.$$

Lean4

/-- Projection of `α` to the closed interval `[a, b]`. -/
def projIcc (a b : α) (h : a ≤ b) (x : α) : Icc a b :=
  ⟨max a (min b x), le_max_left _ _, max_le h (min_le_left _ _)⟩

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