lean_workbook_plus_30240

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that if $f(x)$ is a continuous function on $[a, b]$ and $f(a) \leq f(b)$ , then there exists $c \in [a, b]$ such that $f(c) = f(a) + \frac{f(b) - f(a)}{b - a}(c - a)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30240 (a b : ℝ) (hab : a < b) (f : ℝ → ℝ) (hf : ContinuousOn f (Set.Icc a b)) (h : f a ≤ f b) : ∃ c ∈ Set.Icc a b, f c = f a + (f b - f a) / (b - a) * (c - a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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