author | wenzelm |
Mon, 02 Aug 1999 17:58:46 +0200 | |
changeset 7153 | 820c8c8573d9 |
parent 6892 | 4a905b4a39c8 |
child 7448 | 3ee96dccdd39 |
permissions | -rw-r--r-- |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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(* Title: HOL/Isar_examples/Peirce.thy |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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ID: $Id$ |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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parents:
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Author: Markus Wenzel, TU Muenchen |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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*) |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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|
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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theory Peirce = Main:; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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text {* Peirce's law: examples of classical proof. *}; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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parents:
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theorem "((A --> B) --> A) --> A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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proof; |
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assume aba: "(A --> B) --> A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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show A; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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proof (rule classical); |
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assume not_a: "~ A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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have ab: "A --> B"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
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proof; |
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assume a: A; |
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show B; by contradiction; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
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qed; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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from aba ab; show A; ..; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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qed; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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qed; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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theorem "((A --> B) --> A) --> A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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proof; |
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assume aba: "(A --> B) --> A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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parents:
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show A; |
2ebe9e630cab
Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
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proof (rule classical); |
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presume ab: "A --> B"; |
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from aba ab; show A; ..; |
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next; |
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assume not_a: "~ A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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show "A --> B"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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proof; |
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assume a: A; |
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from not_a a; show B; ..; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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qed; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
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qed; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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qed; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
diff
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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end; |