direct proof

直接证明

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

An argument deriving the conclusion from the given hypotheses by justified steps, without adopting its negation as the main temporary assumption.

从已给假设出发，通过有根据的推理得到结论的一种证明方法。

Example

If a=5ra=5r and b=5sb=5s for integers r,sr,s, then a+b=5(r+s)a+b=5(r+s).

Usage and distinctions

Proving an implication directly still permits assuming its antecedent; direct does not mean assumption-free.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§3.1 Derivations in Natural Deduction; §3.3 Forward and Backward Reasoning · Checked 2026-10-14

Translation sources

  1. 高等教育出版社 — 数学证明 通往高等数学的阶梯（第4版）影印版，官方中文目录官方中文目录：§3.2 直接证明（名称证据，非正文定义证据） · Checked 2026-10-14
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