aksioma sxemasi)
va (2) ga MR qo‘llandi)
aksioma sxemasi)
((3) va (4) ga MR qo‘llandi)
SHunday qilib, biz (1), (2), (3), (4), (5) formulalardan iborat chekli ketma-ketlikni qurdik. Bunda har bir formula yo aksioma, yoki o‘zidan oldingi formulalardan MR qoidasi bo‘yicha hosil qilindi va oxirgi formula teorema ekanini isbotlanishi kerak bo‘lgan formula bilan ustma-ust tushdi.
quyidagi teorema gipotezalardan ko‘p uchraydigan formulalarni keltirib chiqarishga imkon beradi.
Teorema 3.2. (Deduksiya teoremasi). Agar -formulalar to‘plami, va lar esa formulalar bo‘lib , ├ bo‘lsa, u holda ├ ![](data:image/png;base64,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) bo‘ladi. Xususan, agar ├ bo‘lsa, u holda ├![](data:image/png;base64,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) bo‘ladi.
Isbot. Faraz qilaylik ketma-ketlik dan ni keltirib chiqarish bo‘lib, bo‘lsin. bo‘yicha induksiya metodidan foydalanib ├ ![](data:image/png;base64,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) ekanini isbotlaymiz.
bo‘lsin. U holda formula ni dan keltirib chiqarishi bo‘ladi. U holda, ma’lumki formula yo aksioma, yoki ning elementi, yoki bilan ustma-ust tushadi.
ifoda aksioma sxemasidir. SHuning uchun, dastlabki ikki holda quyidagi ketma-ketlik ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAIAAAC0D9CtAAAA5UlEQVR4nGP5//8/A4mAhVQNA6Vn9+7dUVFRb9++RVMkKir68uVL7HpcXV1LS0vfv3/f3t4O5P779+/Xr1+PHz/OyMjA57aLFy/6+vpC2ExMTBwcHLy8vDo6Ovj0XLp0qaamBllEQkJi4sSJOPX8/v370aNH6urqcBFvb++tW7eimYui59q1a58/f2ZhQQi6u7szYAAUPUDPxMXFLViwAMK9e/funDlzCOgBekZPTw/OVVZWhgQgAT0eHh6Yikiwh4CekydPRkdHv3r1ytDQMD09va6ujrAec3PzO3fuELQBi9uIBAAxVFe0LzJpBwAAAABJRU5ErkJggg==) ning dan keltirib chiqarilishi bo‘ladi:
(( ) aksioma sxemasi)
((1), (2) ga MR qo‘llandi)
ya’ni, (dastlabki ikki holda) (1), (2), (3) ketma-ketlik ![](data:image/png;base64,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) formulaning to‘plamdan keltirib chiqarilishi bo‘ladi.
Eslatma. Uchinchi holda ![](data:image/png;base64,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) formulaning dan keltirib chiqarilishi lemma 3.1 ning isbotida qurilgan formulalar ketma-ketligidan isborat.
SHunday qilib bo‘lgan xol isbotlandi.
Endi faraz qilaylik ixtiyoriy bo‘lgan holda ├![](data:image/png;base64,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) bo‘lsin. uchun quyidagi to‘rtta xol bo‘lishi mumkin:
aksioma, yoki , yoki formula bo‘ladi, yoki formula qandaydir va , bu erda formulalardan MR qoidasi bo‘yicha kelib chiqadi va formula ko‘rinishda bo‘ladi. Dastlabki uchta holda ├![](data:image/png;base64,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) ekani xudi dagidek isbotlanadi. Oxirgi xolda esa ├![](data:image/png;base64,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) va ├![](data:image/png;base64,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) larga asoslangan induktiv farazni qo‘llaymiz. aksioma sxemasiga asosan
├![](data:image/png;base64,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) ![](data:image/png;base64,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)
ga ega bo‘lamiz. Bulardan esa ikki marta MR qiodasini qo‘llab, avval ├ ni, so‘ngra ├ ni hosil qilamiz.
SHunday qilib, induksiya metodi bo‘yicha bo‘lgan xol ham isbotlandi.
Natija 3.3. Agar ├![](data:image/png;base64,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) bo‘lsa, u holda , ├ bo‘ladi.
Isbot. Faraz qilaylik ketma-ketlik ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAATCAIAAACY31PkAAABiElEQVR4nGP5//8/Ax0BCz0tG2n27d69Oyoq6u3bt2iKREVFX758SX37XF1dS0tL379/397eDuT++/fv169fjx8/zsjIoIpl6PYBwcWLF319fSFsJiYmDg4OXl5eHR0dUs19/fo1MFQI23fp0qWamhpkEQkJiYkTJ5Jk2fPnzy0tLY8ePSotLY3Pvt+/fz969EhdXR0u4u3tvXXrVpIsAwJJScnc3Fx/f//Dhw9zcnLitO/atWufP39mYUEIuru7k2oZBBQVFR04cCA+Pn7lypWMjIzY7QNGXlxc3IIFCyDcu3fvzpkzhzz7gHYsXLjQ0NCwoaGhsbERu33AyNPT04NzlZWVIQkVE5w8eRIYQ8RY3NHRkZSUJC8vj90+Dw8PYkwxNzcH5hb8as6dOxcRETFjxgy4ZVjsQ/YfJeDgwYM5OTnr16/X1tZGFofaBwyf6OjoV69eAUM8PT29rq6OEsuAJUZra+uuXbuACRVNCmofMHzu3LlDiR3IQFBQEGgZVqkRVT/QAQAARgCQbs+BGk4AAAAASUVORK5CYII=) formulaning dan keltirib chiqarilishi bo‘lsin. U holda, keltirib chiqarishning ta’rifiga asosan formula ![](data:image/png;base64,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) dan iboratdir. Endi esa ning dan keltirib chiqarilishini quramiz:
.
Endi va larga MR qoidasini qo‘llab ga ega bo‘lamiz. Bu esa G dan ning keltirib chiqarilgani ko‘rsatadi.
Natija 3.4. nazariyaning ixtiyoriy formulalari uchun quyidagilar o‘rinlidir:
├
├
isbot. Masalan ning isbotlaylik.
gipoteza
gipoteza
gipoteza
(1) va (3) lar MR qo‘llandi.
(2) va (4) lar MR qo‘llandi.
Demak, ├![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAIAAACw+gCQAAAA70lEQVR4nM2SsQpFYBTHb7nxKiasnoAoHkCZlV0ZzDyGPABlUBaLJ2CwktFgESWDe8pNX7h0dYd7xt/3/Trn/DvPeZ4ft+p5T/sHM4oiRVH6vmcYJk1TgiDCMFRVdRiGlRybgiCYptm2reM4C5EkyTCMruts276YNssyURRRkue5LMsX0y7/oO2GWJZ1YU7TVFUVSZIrGcexrmuUHJtFUUA8OI6jELLBMOzChCUhSdd1V+J5XpIke21rwkoURZ2TjybP8+fkdz3jONY0rWkalmV936dpGu5J1/WFBEGw998mx3FlWaIPcE8bcjbtV/UCKFl5Jj1iJfUAAAAASUVORK5CYII=)
Bunga deduksiya teoremasini qo‘llab
├ ni hosil qilamiz.
(a) bandning isbotini mustaqil bajarish uchun o‘quvchi e’tiboriga xavola etiladi.
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