Ti̍t-chiap chèng-bêng

Tī sò͘-ha̍k kap lô-chek, ti̍t-chiap chèng-bêng (direct proof) sī 1 chióng ti̍t-chiap cho͘-ha̍p kong-siat, tēng-gī, sū-si̍t, sió-tēng-lí (lemma), tēng-lí lâi soeh-bêng 1 ê tîn-su̍t sī chiaⁿ-si̍t--ê ia̍h ké--ê ê koè-têng. Kòe-têng--nih thaû 1 pō͘ kaù kah siōng boé ê kiat-lūn lóng tio̍h-ài ēng ián-e̍k (deduction) ê lô-chek lâi chìn-hêng. Ēng--tio̍h ê lô-chek chha-put-to lóng sī pau-hâm choân-pō͘ ê ... (for all) ia̍h chûn-chāi ... (there exists) ê it-kai lô-chek. Siōng chia̍p ēng--tio̍h ê chèng-bêng kui-chek sī MP (modus ponens), tē 2 chia̍p ēng--ê sī MT (modus tollens); lô-chek choán-oāⁿ (transposition) ham MTP (disjunctive syllogism) mā chin hó-ēng.

Lē

Chit ê lē ēng ti̍t-chiap chèng-bêng lâi chèng-bêng siang-sò͘ ke siang-sò͘ iáu sī siang-sò͘.

Khó-lū 2 ê siang-sò͘ $x$ ham $y$. In-ūi in lóng sī siang-sò͘, ē-tàng kā siá chò $x=2a$ ham $y=2b$, $a$ ham $b$ sī khah sè ê chéng-sò͘. Án-ne, $x+y=2a+2b=2(a+b)$, iā tō sī kóng $x+y$ sī 2 ê poē-sò͘, 1 ê siang-sò͘. Só͘-í 2 ê siang-sò͘ ke chò-hoé tiāⁿ-tio̍h mā sī siang-sò͘.