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6 *) |
6 *) |
7 |
7 |
8 header {* Basic reasoning *}; |
8 header {* Basic reasoning *}; |
9 |
9 |
10 theory BasicLogic = Main:; |
10 theory BasicLogic = Main:; |
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11 |
11 |
12 |
12 subsection {* Some trivialities *}; |
13 subsection {* Some trivialities *}; |
13 |
14 |
14 text {* Just a few toy examples to get an idea of how Isabelle/Isar |
15 text {* Just a few toy examples to get an idea of how Isabelle/Isar |
15 proof documents may look like. *}; |
16 proof documents may look like. *}; |
60 qed; |
61 qed; |
61 qed; |
62 qed; |
62 qed; |
63 qed; |
63 qed; |
64 qed; |
64 |
65 |
65 text {* Variations of backward vs.\ forward reasoning \dots *}; |
66 |
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67 subsection {* Variations of backward vs.\ forward reasoning \dots *}; |
66 |
68 |
67 lemma "A & B --> B & A"; |
69 lemma "A & B --> B & A"; |
68 proof; |
70 proof; |
69 assume "A & B"; |
71 assume "A & B"; |
70 show "B & A"; |
72 show "B & A"; |