Prove2Me

Subadditivity of a truncated sum

Proved
WorkbookSource.problem_53396

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let a≥0, b≥0, c≥0a\geq 0,\ b\geq 0,\ c\geq 0 . Prove that min⁡{a+b, c}≤min⁡{a, c}+min⁡{b, c}\min\{a+b,\ c\}\leq \min\{a,\ c\}+\min\{b,\ c\} .

Source: InternLM Lean-Workbook, record lean_workbook_53396 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.problem_53396 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : min (a + b) c ≤ min a c + min b c  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53396; Apache-2.0

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