`BookProof.ChapterAttentionCollision.log_le_div_add_log_sub_one` {x c : ℝ} (hx : 0 < x) (hc : 0 < c) : Real.log x ≤ x / c + Real.log c - 1

Proved

BookProof.ChapterAttentionCollision.log_le_div_add_log_sub_one

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCollision.

BookProof.ChapterAttentionCollision.log_le_div_add_log_sub_one {x c : ℝ} (hx : 0 < x) (hc : 0 < c) : Real.log x ≤ x / c + Real.log c - 1

Formalization note: Lean 4 identifier BookProof.ChapterAttentionCollision.log_le_div_add_log_sub_one.

Preamble

-- Generated from ChapterAttentionCollision.lean — theorem BookProof.ChapterAttentionCollision.log_le_div_add_log_sub_one
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionCollision
open BookProof.ChapterAttentionCollision


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m : ℕ}

Formal statement

theorem BookProof.ChapterAttentionCollision.log_le_div_add_log_sub_one {x c : ℝ} (hx : 0 < x) (hc : 0 < c) :
    Real.log x ≤ x / c + Real.log c - 1 := by sorry

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