author | wenzelm |
Tue, 05 Oct 1999 18:16:41 +0200 | |
changeset 7740 | 2fbe5ce9845f |
parent 7448 | 3ee96dccdd39 |
child 7748 | 5b9c45b21782 |
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.
wenzelm
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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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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parents:
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section {* Examples of classical proof --- Peirce's law. *}; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
diff
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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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parents:
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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.
wenzelm
parents:
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proof (rule classical); |
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assume "~ A"; |
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have "A --> B"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
diff
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proof; |
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assume A; |
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thus B; by contradiction; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
diff
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qed; |
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with aba; 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:
diff
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
diff
changeset
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theorem "((A --> B) --> A) --> A"; |
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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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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.
wenzelm
parents:
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proof (rule classical); |
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presume "A --> B"; |
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with aba; 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.
wenzelm
parents:
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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; |
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with not_a; show B; ..; |
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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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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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Miscellaneous Isabelle/Isar examples for Higher-Order Logic.
wenzelm
parents:
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end; |