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\u0627\u0633\u062a\u0646\u062a\u0627\u062c. \u0627\u0644\u0622\u0644\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 \u0628\u0646\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0647\u064a \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a \u0627\u0644\u0631\u0633\u0645\u064a.<\/strong><\/span><\/p>\n<a name=\"1\"><\/a><\/p>\n<h2>\u0645\u0627 \u0647\u0648 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a \u0627\u0644\u0631\u0633\u0645\u064a\u061f<\/h2>\n\u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a\u0629 \u0627\u0644\u0631\u0633\u0645\u064a\u0629\u060c \u0623\u0648 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a\u060c \u0644\u0647\u0627 \u062b\u0644\u0627\u062b\u0629 \u0645\u0643\u0648\u0646\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629:<\/span><\/p>\n<ol style=\"color: #000000; text-align: justify;\">\n<li>\u0644\u063a\u0629 \u0631\u0633\u0645\u064a\u0629.<\/strong><\/li>\n<li>\u0645\u062e\u0637\u0637 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a\u064a.<\/strong><\/li>\n<li>\u0642\u0648\u0627\u0639\u062f \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0623\u0648\u0644\u064a\u0629.<\/strong><\/li>\n<\/ol>\n\u0644\u0642\u062f \u0631\u0627\u062c\u0639\u0646\u0627 \u0628\u0627\u0644\u0641\u0639\u0644 \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0627\u0644\u0644\u063a\u0627\u062a \u0627\u0644\u0631\u0633\u0645\u064a\u0629. \u0627\u0644\u0622\u0646 \u062f\u0648\u0631\u0646\u0627 \u0644\u0646\u0642\u062f\u0645 \u0645\u062e\u0637\u0637\u0627\u062a \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0648\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u0623\u0648\u0644\u064a\u0629.<\/span><\/p>\n\u0644\u0628\u0646\u0627\u0621 \u0646\u0638\u0627\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a \u0633\u0646\u0628\u062f\u0623 \u0628\u062a\u062c\u0645\u064a\u0639 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a \u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a <a href=\"https:\/\/es.wikipedia.org\/wiki\/Jan_%C5%81ukasiewicz\" rel=\"noopener\" target=\"_blank\">\u0141ukasiewicz<\/a><\/strong>, \u0648\u0643\u0642\u0627\u0639\u062f\u0629 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0623\u0648\u0644\u064a\u0629 \u0633\u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633.<\/strong><\/span><\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=206s\" target=\"_blank\" rel=\"noopener\">\u0625\u0630\u0627 \u0643\u0627\u0646 \\alpha, \\beta<\/span> \u0648 \\gamma<\/span> \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a\u060c<\/span><\/strong><\/a> \u0641\u0625\u0646 \u0627\u0644\u0622\u062a\u064a \u0647\u0648 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a:<\/span><\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td>[A1]<\/td>\n<td>(\\alpha \\rightarrow (\\beta \\rightarrow \\alpha))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A2]<\/td>\n<td>((\\alpha \\rightarrow (\\beta \\rightarrow \\gamma))\\rightarrow ((\\alpha\\rightarrow \\beta)\\rightarrow(\\alpha \\rightarrow \\gamma)))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A3]<\/td>\n<td>((\\neg\\beta \\rightarrow \\neg\\alpha)\\rightarrow(\\alpha\\rightarrow \\beta))<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"3\"><\/a><\/p>\n<h2>\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633: \u0627\u0644\u0645\u062d\u0631\u0643 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=392s\" target=\"_blank\" rel=\"noopener\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \\alpha<\/span> \u0648 \\beta<\/span> \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0635\u0627\u0644\u062d\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a\u060c<\/span> <\/strong><\/a>\u064a\u0646\u0635 \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0645\u0646 \\alpha<\/span> \u0648 (\\alpha \\rightarrow \\beta)<\/span> \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \\beta<\/span>. \u064a\u062a\u0645 \u0643\u062a\u0627\u0628\u0629 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/span><\/p>\n<table style=\"color: #000000; text-align: justify;\">\n<caption>\u0647\u064a\u0643\u0644 \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633<\/caption>\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\alpha<\/span><\/td>\n<td>; \u0627\u0644\u0641\u0631\u0636\u064a\u0629<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td>(\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u0627\u0644\u0641\u0631\u0636\u064a\u0629<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td>\\beta<\/span><\/td>\n<td>; MP(1,2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0647\u0646\u0627 \u062a\u0645 \u0627\u062e\u062a\u0635\u0627\u0631 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a (1) \u0648 (2) \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0643\u062a\u0627\u0628\u0629 \u00abMP(1,2)\u00bb\u060c \u0648\u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644 \u062e\u0644\u0627\u0635\u0629 \u0643\u0644 \u0647\u0630\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u062f\u0648\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n\u0644\u0630\u0644\u0643 \\{\\alpha, (\\alpha \\rightarrow \\beta)\\}\\vdash \\beta <\/span>\n\u0633\u0646\u0631\u0649 \u0642\u0631\u064a\u0628\u064b\u0627 \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0628\u0646\u0627\u0621 \u062c\u0645\u064a\u0639 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a \u0645\u0646 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u062c\u0645\u0639 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0639\u0627\u062f\u064a \u0648\u062a\u0634\u0643\u0644 \u0627\u0644\u0623\u0633\u0627\u0633 \u0644\u0640 \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a.<\/strong><\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>\u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u0648\u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0648\u0627\u0644\u0641\u0631\u0648\u0636<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=506s\" target=\"_blank\" rel=\"noopener\">\u0641\u064a \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0644\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a \u064a\u062a\u0645 \u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a<\/span><\/strong><\/a> (\u0623\u0648 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a)\u060c \u0648\u0647\u0630\u0647 \u0647\u064a \u0623\u064a \u062a\u062a\u0627\u0628\u0639 \u0644\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u062d\u064a\u062b \u0643\u0644 \u0645\u0646\u0647\u0627 \u0625\u0645\u0627 \u0641\u0631\u0636\u064a\u0629 \u0623\u0648 \u062a\u0639\u0628\u064a\u0631 \u0645\u0633\u062a\u062d\u0635\u0644 \u0645\u0646 \u0627\u0644\u0641\u0631\u0648\u0636 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0641\u0642\u0637 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633. \u0646\u0638\u0631\u064a\u0629 \u0647\u064a \u0646\u062a\u064a\u062c\u0629 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0628\u062f\u0648\u0646 \u0641\u0631\u0648\u0636. \u0627\u0644\u0641\u0631\u0636\u064a\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0623\u064a \u062a\u0639\u0628\u064a\u0631 \u0644\u064a\u0633 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u064b \u0648\u0644\u0627 \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647 \u0645\u0646\u0647\u0627. \u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0641\u0631\u0648\u0636 \\Gamma<\/span> \u0648\u062a\u0639\u0628\u064a\u0631 \\alpha<\/span> \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0628\u0639\u0636 \u0639\u0646\u0627\u0635\u0631 \\Gamma<\/span> \u0648\u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633\u060c \u0646\u0643\u062a\u0628 \u00ab\\Gamma \\vdash \\alpha<\/span>\u00bb \u0648\u0646\u0642\u0648\u0644 \u0623\u0646<\/p>\n\u0645\u0646 \\Gamma<\/span> \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c <\/em>\\alpha<\/span>\n\u0625\u0630\u0627 \u0643\u0627\u0646 \\Gamma<\/span> \u0645\u062c\u0645\u0648\u0639\u0629 \u0641\u0627\u0631\u063a\u0629\u060c \u0641\u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0643\u062a\u0627\u0628\u0629 \u00ab\\emptyset\\vdash \\alpha<\/span>\u00bb \u0646\u0643\u062a\u0628 \u00ab \\vdash \\alpha <\/span>.\u00bb \u0648\u0647\u0630\u0627 \u064a\u064f\u0642\u0631\u0623 \u00ab\\alpha<\/span> \u0647\u064a \u0646\u0638\u0631\u064a\u0629\u00bb. \u064a\u0645\u0643\u0646 \u062a\u0648\u0633\u064a\u0639 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0641\u064a \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0628\u062d\u064a\u062b \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \\alpha<\/span> \u0648 \\beta<\/span> \u0648 \\gamma<\/span> \u062a\u0639\u0628\u064a\u0631\u0627\u062a\u060c \u0641\u0625\u0646 \u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz \u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u062a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>[A1]<\/td>\n<td>\\vdash (\\alpha \\rightarrow (\\beta \\rightarrow \\alpha))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A2]<\/td>\n<td>\\vdash((\\alpha \\rightarrow (\\beta \\rightarrow \\gamma))\\rightarrow ((\\alpha\\rightarrow \\beta)\\rightarrow(\\alpha \\rightarrow \\gamma)))<\/span><\/td>\n<\/tr>\n<tr>\n<td>[A3]<\/td>\n<td>\\vdash((\\neg\\beta \\rightarrow \\neg\\alpha)\\rightarrow(\\alpha\\rightarrow \\alpha))<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0648\u0645\u0646 \u0647\u0630\u0627 \u064a\u0642\u0627\u0644 \u0625\u0646 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0647\u064a \u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0627\u0636\u062d\u0629 \u0628\u062d\u062f \u0630\u0627\u062a\u0647\u0627\u060c \u0623\u0648 \u0623\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0647\u064a \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647\u0627 \u0645\u0646 \u0641\u0631\u0627\u063a\u060c \u0623\u0648 \u0623\u0646 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0648\u0627\u0644\u0646\u0638\u0631\u064a\u0627\u062a \u0647\u064a \u062e\u0635\u0627\u0626\u0635 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a.<\/p>\n<a name=\"5\"><\/a><\/p>\n<h2>\u0643\u064a\u0641 \u064a\u062a\u0645 \u062a\u0646\u0641\u064a\u0630 \u062f\u0644\u064a\u0644 \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a\u061f<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=783s\" target=\"_blank\" rel=\"noopener\">\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u062d\u0644\u0629 \u0633\u0646\u062a\u0648\u0642\u0641 \u0639\u0646 \u0627\u0644\u062d\u062f\u064a\u062b \u0639\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0648\u0646\u0646\u062a\u0642\u0644 \u0625\u0644\u0649 \u0627\u0644\u0639\u0645\u0644 \u0627\u0644\u0639\u0645\u0644\u064a.<\/span><\/strong><\/a> \u0648\u0647\u0648 \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0627\u0644\u0642\u0648\u0644 \u0627\u0644\u0643\u062b\u064a\u0631 \u0639\u0646 \u062a\u0646\u0641\u064a\u0630 \u062f\u0644\u064a\u0644\u061b \u0644\u0643\u0646 \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0645\u0627 \u064a\u0642\u0627\u0644 \u0639\u0646 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a\u060c \u0648\u062d\u062a\u0649 \u0625\u0630\u0627 \u062a\u0645 \u0641\u0647\u0645 \u0643\u0644 \u0634\u064a\u0621\u060c \u0647\u0630\u0627 \u0644\u0627 \u064a\u0639\u0646\u064a \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0623\u0646\u0647 \u064a\u062a\u0645 \u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u0643\u0641\u0627\u0621\u0627\u062a \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u062a\u0646\u0641\u064a\u0630 \u062f\u0644\u064a\u0644. \u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628\u060c \u0644\u062a\u0639\u0644\u064a\u0645 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0628\u0647\u0627 \u0639\u0645\u0644 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646\u060c \u0633\u0646\u0631\u0627\u062c\u0639 \u0628\u0631\u0647\u0627\u0646\u064b\u0627 \u0628\u0633\u064a\u0637\u064b\u0627 \u0644\u0646\u0638\u0631\u064a\u0629.<\/p>\n\u0646\u0638\u0631\u064a\u0629<\/strong><\/p>\n\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \\alpha<\/span> \u062a\u0639\u0628\u064a\u0631\u064b\u0627 \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a\u060c \u0641\u0625\u0646\u0647 \u064a\u062a\u0645 \u0627\u0644\u0648\u0641\u0627\u0621 \u0628\u0645\u0627 \u064a\u0644\u064a<\/p>\n\\vdash (\\alpha\\rightarrow \\alpha)<\/span>\n\u0628\u0631\u0647\u0627\u0646<\/strong><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td> (\\alpha\\rightarrow ( \\alpha \\rightarrow \\alpha)) <\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td> (\\alpha\\rightarrow ((\\alpha\\rightarrow \\alpha)\\rightarrow\\alpha)) <\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td> ( (\\alpha\\rightarrow((\\alpha\\rightarrow\\alpha)\\rightarrow\\alpha)) \\rightarrow ((\\alpha\\rightarrow (\\alpha\\rightarrow\\alpha))\\rightarrow( \\alpha\\rightarrow \\alpha))) <\/span><\/td>\n<td>; A2<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td> ((\\alpha\\rightarrow (\\alpha\\rightarrow\\alpha))\\rightarrow( \\alpha\\rightarrow \\alpha)) <\/span><\/td>\n<td>; MP(2,3)<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td> ( \\alpha\\rightarrow \\alpha) <\/span><\/td>\n<td>; MP(1,5)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0644\u0630\u0644\u0643 \\vdash (\\alpha\\rightarrow\\alpha)<\/span>\n\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0628\u0631\u0647\u0627\u0646.<\/p>\n\u0643\u0645\u0627 \u064a\u0645\u0643\u0646 \u0631\u0624\u064a\u0629 \u0630\u0644\u0643\u060c \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a\u060c \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0644\u064a\u0633\u062a \u0628\u0633\u064a\u0637\u0629\u060c \u0648\u0644\u0643\u0646 \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u064a\u062a\u0645 \u0628\u0646\u0627\u0624\u0647\u0627 \u062a\u0635\u0628\u062d \u0633\u0647\u0644\u0629 \u0627\u0644\u062a\u0643\u0631\u0627\u0631.<\/p>\n\u0627\u0644\u0622\u0646\u060c \u0642\u0628\u0644 \u0623\u0646 \u0646\u0628\u062f\u0623 \u0641\u064a \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a\u060c \u0633\u0646\u0637\u0648\u0631 \u0623\u0648\u0644\u0627\u064b \u0628\u0639\u0636 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0648\u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0627\u0644\u062a\u064a \u0633\u062a\u0643\u0648\u0646 \u0645\u0641\u064a\u062f\u0629 \u0644\u0644\u063a\u0627\u064a\u0629 \u0644\u0647\u0630\u0627 \u0627\u0644\u0639\u0645\u0644\u060c \u0644\u0623\u0646\u0647 \u0625\u0630\u0627 \u0631\u0643\u0632\u0646\u0627 \u0641\u0642\u0637 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0641\u0642\u062f \u0646\u0648\u0627\u062c\u0647 \u0645\u0634\u0627\u0643\u0644 \u0643\u0628\u064a\u0631\u0629.<\/p>\n<a name=\"6\"><\/a><\/p>\n<h2>\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062a\u0643\u0627\u0641\u0624 \u0627\u0644\u0645\u062b\u0628\u062a<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1191s\" target=\"_blank\" rel=\"noopener\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \\alpha<\/span> \u0648 \\beta<\/span> \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0648\u064a\u062a\u062d\u0642\u0642 \u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0648\u0642\u062a<\/span> <\/strong><\/a>\u0623\u0646 \\{\\alpha\\}\\vdash \\beta<\/span> \u0648 \\{\\beta\\} \\vdash \\alpha<\/span>\u060c \u0641\u0625\u0646\u0647 \u064a\u0642\u0627\u0644 \u0625\u0646 \\alpha<\/span> \u0648 \\beta<\/span> \u0645\u062a\u0643\u0627\u0641\u0626\u062a\u0627\u0646 \u0645\u062b\u0628\u062a\u062a\u0627\u0646 \u0648\u064a\u0643\u062a\u0628 \\alpha \\dashv \\vdash \\beta<\/span>. \u0648\u064a\u0645\u0643\u0646 \u062a\u0644\u062e\u064a\u0635 \u0647\u0630\u0627 \u0631\u0645\u0632\u064a\u0627\u064b \u0643\u0627\u0644\u0622\u062a\u064a:<\/p>\n\\left(\\{\\alpha\\}\\vdash\\beta \\wedge \\{\\beta\\}\\vdash\\alpha \\right) \\Leftrightarrow \\left(\\alpha\\dashv\\vdash\\beta\\right)<\/span>\n\u0648\u0647\u0630\u0627 \u064a\u064f\u0642\u0631\u0623: \u0645\u0646 \\alpha<\/span> \u064a\u064f\u0633\u062a\u0646\u062a\u062c \\beta<\/span>\u060c \u0648\u0645\u0646 \\beta<\/span> \u064a\u064f\u0633\u062a\u0646\u062a\u062c \\alpha<\/span> \u0625\u0630\u0627 \u0648\u0641\u0642\u0637 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \\alpha<\/span> \u0648 \\beta<\/span> \u0645\u062a\u0643\u0627\u0641\u0626\u062a\u064a\u0646 \u0645\u062b\u0628\u062a\u062a\u064a\u0646.<\/p>\n\u0647\u0630\u0647 \u062e\u0627\u0635\u064a\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a<\/p>\n<a name=\"7\"><\/a><\/p>\n<h2>\u0627\u0644\u0645\u064a\u062a\u0627-\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1355s\" target=\"_blank\" rel=\"noopener\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \\alpha<\/span> \u0648 \\beta<\/span> \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0627\u062a\u060c<\/span><\/strong><\/a> \u0648 \\Gamma<\/span> \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0641\u0631\u0648\u0636\u061b \u0641\u0625\u0646\u0647 \u064a\u064f\u0642\u0627\u0644 \u0625\u0630\u0627 \u0645\u0646 \\Gamma \\cup \\{\\alpha\\}<\/span> \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \\beta<\/span>\u060c \u0641\u0625\u0646\u0647 \u0645\u0646 \\Gamma<\/span> \u064a\u064f\u0633\u062a\u0646\u062a\u062c (\\alpha \\rightarrow \\beta)<\/span>. \u0648\u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646 \u0647\u0630\u0627 \u0631\u0645\u0632\u064a\u0627\u064b \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n\\left(\\Gamma \\cup \\{\\alpha\\}\\vdash \\beta \\right) \\Rightarrow \\left( \\Gamma\\vdash(\\alpha\\rightarrow\\beta)\\right)\n\n<\/span>\n\u0628\u0631\u0647\u0627\u0646:<\/strong><\/p>\n\u0644\u0643\u064a \u064a\u062a\u062d\u0642\u0642 \\Gamma \\cup \\{\\alpha\\}\\vdash \\beta<\/span>\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 \u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\gamma_1<\/span><\/td>\n<td>; \u0641\u0631\u0636\u064a\u0629 1 \u0645\u0646 \\Gamma<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\vdots<\/span><\/td>\n<td>\\vdots<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(n)<\/td>\n<td>\\gamma_n<\/span><\/td>\n<td>; \u0641\u0631\u0636\u064a\u0629 n \u0645\u0646 \\Gamma<\/span><\/td>\n<\/tr>\n<tr>\n<td>(n+1)<\/td>\n<td>\\overline{\\gamma}_1<\/span><\/td>\n<td>; \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 \u0628\u064a\u0646 \u0632\u0648\u062c\u064a\u0646 \u0645\u0646 \u0627\u0644\u0633\u0637\u0648\u0631 \u0627\u0644\u0633\u0627\u0628\u0642\u0629<\/td>\n<\/tr>\n<tr>\n<td>\\vdots<\/span><\/td>\n<td>\\vdots<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(n+m)<\/td>\n<td>\\overline{\\gamma}_m<\/span><\/td>\n<td>; \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 \u0628\u064a\u0646 \u0632\u0648\u062c\u064a\u0646 \u0645\u0646 \u0627\u0644\u0633\u0637\u0648\u0631 \u0627\u0644\u0633\u0627\u0628\u0642\u0629<\/td>\n<\/tr>\n<tr>\n<td>(n+m+1)<\/td>\n<td>\\alpha<\/span><\/td>\n<td>; \u0641\u0631\u0636\u064a\u0629<\/td>\n<\/tr>\n<tr>\n<td>(n+m+2)<\/td>\n<td>\\beta<\/span><\/td>\n<td>; \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 (n+m+1, \u0623\u062d\u062f \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060c \u0628\u0627\u0633\u062a\u062b\u0646\u0627\u0621 n+m+1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0644\u0630\u0644\u0643 \\Gamma\\cup\\{\\alpha\\} \\vdash \\beta <\/span>\n\u0644\u0643\u064a \u064a\u0643\u0648\u0646 \u0647\u0630\u0627 \u0645\u0645\u0643\u0646\u0627\u064b\u060c \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0623\u0646 \u062a\u0643\u0648\u0646 \u0648\u0627\u062d\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0645\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \\gamma_1, \\cdots \\gamma_n,\\overline{\\gamma_1},\\cdots,\\overline{\\gamma_m}<\/span> \u0639\u0644\u0649 \u0634\u0643\u0644 (\\alpha\\rightarrow \\beta)<\/span>\u060c \u0648\u0644\u0643\u0646 \u0643\u0644 \u0647\u0630\u0647 \u0627\u0644\u0623\u0633\u0637\u0631 \u062a\u062a\u0636\u0645\u0646 \u0641\u0642\u0637 \u0639\u0646\u0627\u0635\u0631 \u0645\u0646 \\Gamma<\/span> \u0648\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz \u0641\u064a \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0647\u0627\u060c \u0644\u0630\u0627 \u064a\u062c\u0628 \u0623\u0646 \u064a\u062a\u062d\u0642\u0642 \\Gamma\\vdash (\\alpha \\rightarrow \\beta)<\/span>. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u064a\u062b\u0628\u062a \u0627\u0644\u0646\u0638\u0631\u064a\u0629<\/p>\n\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0628\u0631\u0647\u0627\u0646.<\/p>\n<a name=\"8\"><\/a><\/p>\n<h2>\u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1668s\" target=\"_blank\" rel=\"noopener\">\u0641\u064a \u0646\u0641\u0633 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0645\u0648\u0636\u0648\u0639\u0629 \u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u060c \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0645\u0627 \u064a\u0644\u064a<\/span><\/strong><\/a><\/p>\n\n\\left(\\Gamma\\vdash(\\alpha \\rightarrow \\beta)\\right) \\Rightarrow \\left( \\Gamma \\cup \\{\\alpha\\}\\vdash \\beta \\right)\n\n<\/span>\n\u0628\u0631\u0647\u0627\u0646:<\/strong><\/p>\n\u0625\u0630\u0627 \u062a\u062d\u0642\u0642 \\Gamma\\vdash (\\alpha\\rightarrow \\beta)<\/span>\u060c \u0641\u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0628\u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\gamma_1<\/span><\/td>\n<td>; \u0627\u0644\u0641\u0631\u0636\u064a\u0629 1 \u0645\u0646 \\Gamma<\/span><\/td>\n<\/tr>\n<tr>\n<td>\\vdots<\/span><\/td>\n<td>\\vdots<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>(n)<\/td>\n<td>\\gamma_n<\/span><\/td>\n<td>; \u0627\u0644\u0641\u0631\u0636\u064a\u0629 n \u0645\u0646 \\Gamma<\/span><\/td>\n<\/tr>\n<tr>\n<td>(n+1)<\/td>\n<td>(\\alpha \\rightarrow \\beta)<\/span><\/td>\n<td>; \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 (\u0628\u064a\u0646 \u0632\u0648\u062c \u0645\u0646 \u0627\u0644\u0633\u0637\u0648\u0631 \u0627\u0644\u0633\u0627\u0628\u0642\u0629)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0627\u0644\u0622\u0646\u060c \u0625\u0630\u0627 \u0623\u0636\u0641\u0646\u0627 \\alpha<\/span> \u0643\u0641\u0631\u0636\u064a\u0629 \u0625\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u060c \u0641\u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u0633\u0637\u0648\u0631 \u0627\u0644\u062a\u0627\u0644\u064a\u0629<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(n+2)<\/td>\n<td>\\alpha<\/span><\/td>\n<td>; \u0641\u0631\u0636\u064a\u0629 \u0625\u0636\u0627\u0641\u064a\u0629<\/td>\n<\/tr>\n<tr>\n<td>(n+3)<\/td>\n<td>\\beta<\/span><\/td>\n<td>; \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633(n+1,n+2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0644\u0630\u0644\u0643 \\Gamma \\cup \\{\\alpha\\} \\vdash \\beta<\/span>\n\u0648\u0647\u0630\u0627 \u0645\u0627 \u0643\u0646\u0627 \u0646\u0631\u063a\u0628 \u0641\u064a \u0625\u062b\u0628\u0627\u062a\u0647.<\/p>\n\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0628\u0631\u0647\u0627\u0646.<\/p>\n<a name=\"9\"><\/a><\/p>\n<h2>\u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u062d\u0648\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0648\u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u062d\u0648\u0644 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a<\/h2>\n\u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0645\u062b\u0644 \u0627\u0644\u062a\u064a \u062a\u0645 \u0625\u062c\u0631\u0627\u0624\u0647\u0627 \u0633\u0627\u0628\u0642\u064b\u0627 \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \\vdash (\\alpha\\rightarrow \\alpha)<\/span> \u0647\u064a \u062d\u0627\u0644\u0627\u062a \u0644\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u0628\u0646\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a\u060c \u0644\u0623\u0646 \u0643\u0644 \u062e\u0637\u0648\u0629 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u062a\u0639\u0628\u064a\u0631 \u0645\u062d\u062f\u062f. \u0628\u0637\u0631\u064a\u0642\u0629 \u0645\u0645\u0627\u062b\u0644\u0629\u060c \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0625\u062c\u0631\u0627\u0621 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u0645\u0628\u0646\u064a\u0629 \u0639\u0644\u0649 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u0623\u062e\u0631\u0649\u060c \u062d\u064a\u062b \u064a\u0643\u0648\u0646 \u0643\u0644 \u062e\u0637\u0648\u0629 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064b\u0627 \u0641\u064a \u062d\u062f \u0630\u0627\u062a\u0647. \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0643\u0644\u0627 \u0627\u0644\u0623\u0645\u0631\u064a\u0646 \u064a\u062a\u0645 \u0625\u062c\u0631\u0627\u0624\u0647\u0645\u0627 \u0628\u0637\u0631\u064a\u0642\u0629 \u0645\u0645\u0627\u062b\u0644\u0629\u060c \u0644\u0643\u0646 \u0627\u0644\u062b\u0627\u0646\u064a \u064a\u062a\u064a\u062d \u0644\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0648\u0646\u0638\u064a\u0631\u062a\u0647\u0627\u060c \u0645\u0645\u0627 \u064a\u0645\u0646\u062d \u0645\u0631\u0648\u0646\u0629 \u0643\u0628\u064a\u0631\u0629 \u0644\u062a\u0642\u0646\u064a\u0629 \u0627\u0644\u062a\u0641\u0643\u064a\u0631. \u0644\u0646\u0631\u0649 \u0630\u0644\u0643\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u062b\u0628\u062a \u0645\u0631\u0629 \u0623\u062e\u0631\u0649 \u0623\u0646 \\vdash (\\alpha \\rightarrow \\alpha)<\/span>\u060c \u0648\u0644\u0643\u0646 \u0627\u0644\u0622\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644\u0627\u062a \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a. \u0628\u062f\u064a\u0644 \u0644\u0630\u0644\u0643 \u0647\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td>\\vdash (\\alpha \\rightarrow (\\alpha \\rightarrow \\alpha))<\/span><\/td>\n<td>; A1<\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td>\\{\\alpha\\}\\vdash ( \\alpha \\rightarrow \\alpha)<\/span><\/td>\n<td>; RTD(1)<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td>\\{\\alpha\\}\\cup \\{\\alpha\\}\\vdash \\alpha<\/span><\/td>\n<td>; RTD(2)<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td>\\{\\alpha\\}\\vdash \\alpha<\/span><\/td>\n<td>; \u0644\u0627\u062d\u0638 \u0623\u0646 \\{\\alpha\\}\\cup\\{\\alpha\\}=\\{\\alpha\\}<\/span><\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td>\\vdash (\\alpha\\rightarrow \\alpha)<\/span><\/td>\n<td>; TD(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0644\u0627\u062d\u0638 \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0644\u064a\u0633 \u0623\u0642\u0635\u0631 \u0645\u0646 \u0627\u0644\u0630\u064a \u0642\u0645\u0646\u0627 \u0628\u0647 \u0633\u0627\u0628\u0642\u064b\u0627\u060c \u0644\u0643\u0646\u0647 \u0623\u0633\u0647\u0644 \u0628\u0643\u062b\u064a\u0631 \u0644\u0644\u0642\u064a\u0627\u0645 \u0628\u0647\u060c \u062d\u064a\u062b \u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0627 \u0641\u0642\u0637 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0648\u0646\u0638\u064a\u0631\u062a\u0647\u0627 \u0648\u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u064a A1 \u0644\u0628\u0646\u0627\u0621 \u0627\u0644\u0628\u0631\u0647\u0627\u0646.<\/p>\n\u0641\u064a \u0627\u0644\u0638\u0627\u0647\u0631\u060c \u0641\u064a \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u0630\u064a \u0642\u0645\u0646\u0627 \u0628\u0647 \u0644\u0644\u062a\u0648 \u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0627 \u0623\u0643\u0633\u064a\u0648\u0645\u0627 \u0648\u0627\u062d\u062f\u064b\u0627 \u0645\u0646 \u0141ukasiewicz \u0648\u062a\u062c\u0627\u0647\u0644\u0646\u0627 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633. \u0647\u0644 \u064a\u0639\u0646\u064a \u0630\u0644\u0643 \u0623\u0646\u0646\u0627 \u0628\u062a\u0641\u0643\u064a\u0631\u0646\u0627 \u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0646\u062a\u062c\u0627\u0647\u0644 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633\u061f \u0627\u0644\u0625\u062c\u0627\u0628\u0629 \u0646\u0639\u0645 \u0648\u0644\u0627. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062a\u0638\u0627\u0647\u0631 \u0628\u0623\u0646\u0646\u0627 \u0646\u062a\u062c\u0627\u0647\u0644 \u0628\u0639\u0636 \u0627\u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 \u0644\u0623\u0646\u0646\u0627 \u0644\u0627 \u0646\u0633\u062a\u062e\u062f\u0645\u0647\u0627 \u0628\u0634\u0643\u0644 \u0635\u0631\u064a\u062d\u060c \u0648\u0644\u0643\u0646 \u064a\u062c\u0628 \u0623\u0646 \u0646\u062a\u0630\u0643\u0631 \u0623\u0646 \u0643\u0644\u064b\u0627 \u0645\u0646 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0648\u0646\u0638\u064a\u0631\u062a\u0647\u0627 \u0647\u064a \u0646\u062a\u064a\u062c\u0629 \u0644\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz \u0648\u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633\u060c \u0645\u0645\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627\u060c \u0643\u0645\u0627 \u0641\u0639\u0644\u0646\u0627 \u0641\u064a \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0627\u0644\u0630\u064a \u0631\u0623\u064a\u0646\u0627 \u0644\u0644\u062a\u0648\u060c \u064a\u0639\u062a\u0628\u0631 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u064b\u0627 \u0636\u0645\u0646\u064a\u064b\u0627 \u0644\u0647\u0627.<\/p>\n<a name=\"10\"><\/a><\/p>\n<h2>\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u062a\u0645\u0627\u062b\u0644<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1972s\" target=\"_blank\" rel=\"noopener\">\u0625\u0630\u0627 \u0643\u0627\u0646 \\tau<\/span> \u0646\u0638\u0631\u064a\u0629\u060c<\/span><\/strong><\/a> \u0641\u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0623\u0646\u0647\u060c \u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0623\u064a \u062a\u0639\u0628\u064a\u0631 \\beta<\/span>\u060c \u0633\u064a\u062a\u062d\u0642\u0642 \u0645\u0627 \u064a\u0644\u064a<\/p>\n\\{\\beta\\}\\vdash\\tau<\/span>\n\u0647\u0630\u0647 \u0641\u064a \u0627\u0644\u062d\u0642\u064a\u0642\u0629 \u0642\u0627\u0639\u062f\u0629 \u0633\u0647\u0644\u0629 \u062c\u062f\u064b\u0627 \u0644\u0644\u0625\u062b\u0628\u0627\u062a\u060c \u062d\u064a\u062b \u0623\u0646 \\tau<\/span> \u0643\u0648\u0646\u0647\u0627 \u0646\u0638\u0631\u064a\u0629\u060c \u0633\u064a\u062a\u062d\u0642\u0642 \u0623\u0646 \\vdash \\tau<\/span>. \u0623\u064a \u0623\u0646\u0647 \u064a\u0648\u062c\u062f \u0627\u0633\u062a\u062f\u0644\u0627\u0644 \u0644\u0627 \u064a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0625\u0636\u0627\u0641\u0629 \u0641\u0631\u0648\u0636 \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \\tau<\/span>\u060c \u0644\u0630\u0627 \u0625\u0636\u0627\u0641\u0629 \u062a\u0639\u0628\u064a\u0631 \u0625\u0636\u0627\u0641\u064a \u0625\u0644\u0649 \u0627\u0644\u0641\u0631\u0648\u0636 (\u0627\u0644\u0641\u0627\u0631\u063a\u0629) \u0644\u0646 \u064a\u062e\u0644\u0642 \u0641\u0631\u0642\u064b\u0627.<\/p>\n\u0628\u0637\u0631\u064a\u0642\u0629 \u0645\u0645\u0627\u062b\u0644\u0629 \u0644\u0647\u0630\u0627 \u064a\u0645\u0643\u0646 \u0637\u0631\u062d \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: \u0625\u0630\u0627 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0641\u0631\u0648\u0636 \\Gamma<\/span> \u064a\u062a\u0645 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \\gamma<\/span>\u060c \u0641\u0633\u064a\u062a\u062d\u0642\u0642 \u0645\u0627 \u064a\u0644\u064a<\/p>\n\\Gamma\\cup\\{\\alpha\\}\\vdash\\gamma<\/span>\n\u062d\u064a\u062b \u0623\u0646 \\alpha<\/span> \u0647\u0648 \u062a\u0639\u0628\u064a\u0631 \u0623\u064a\u064b\u0627 \u0643\u0627\u0646.<\/p>\n<a name=\"11\"><\/a><\/p>\n<h2>\u062a\u0631\u0643\u064a\u0628 \u0648\u062a\u0623\u0645\u0644\u0627\u062a \u062d\u0648\u0644 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=OvoEDefcSZg&t=1933s\" target=\"_blank\" rel=\"noopener\">\u0639\u0646\u062f\u0645\u0627 \u0646\u0645\u0646\u062d \u0644\u063a\u0629 \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u062d\u064a \u0642\u0627\u0639\u062f\u0629 \u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0648\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629:<\/span><\/strong><\/a> \u0627\u0644\u0645\u0648\u062f\u0633 \u0628\u0648\u0646\u0646\u0633 \u0648\u0623\u0643\u0633\u064a\u0648\u0645\u0627\u062a \u0141ukasiewicz\u060c \u0645\u0627 \u0646\u0642\u0648\u0645 \u0628\u0647 \u064a\u0634\u0628\u0647 \u0628\u0646\u0627\u0621 \u00ab\u0622\u0644\u0629 \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u064a\u0629\u00bb \u0648\u00bb\u0645\u062d\u0631\u0643 \u064a\u0632\u0648\u062f\u0647\u0627 \u0628\u0627\u0644\u0637\u0627\u0642\u0629 \u0644\u0644\u062f\u062e\u0648\u0644 \u0641\u064a \u0627\u0644\u062d\u0631\u0643\u0629\u00bb. \u0645\u0646 \u0647\u0646\u0627 \u062a\u0628\u062f\u0623 \u062c\u0645\u064a\u0639 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0641\u064a \u0627\u0644\u0638\u0647\u0648\u0631 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a 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