| author | paulson |
| Fri, 29 Oct 2004 15:16:02 +0200 | |
| changeset 15270 | 8b3f707a78a7 |
| parent 14126 | 28824746d046 |
| child 16417 | 9bc16273c2d4 |
| permissions | -rw-r--r-- |
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(* Title: HOL/ex/Puzzle.thy |
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ID: $Id$ |
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Author: Tobias Nipkow |
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Copyright 1993 TU Muenchen |
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A question from "Bundeswettbewerb Mathematik" |
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Proof due to Herbert Ehler |
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*) |
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theory Puzzle = Main: |
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consts f :: "nat => nat" |
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Tidying and replacement of some axioms by specifications
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specification (f) |
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28824746d046
Tidying and replacement of some axioms by specifications
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f_ax [intro!]: "f(f(n)) < f(Suc(n))" |
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Tidying and replacement of some axioms by specifications
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by (rule exI [of _ id], simp) |
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lemma lemma0 [rule_format]: "\<forall>n. k=f(n) --> n <= f(n)" |
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apply (induct_tac "k" rule: nat_less_induct) |
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apply (rule allI) |
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apply (rename_tac "i") |
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apply (case_tac "i") |
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apply simp |
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apply (blast intro!: Suc_leI intro: le_less_trans) |
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done |
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lemma lemma1: "n <= f(n)" |
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by (blast intro: lemma0) |
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lemma lemma2: "f(n) < f(Suc(n))" |
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by (blast intro: le_less_trans lemma1) |
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lemma f_mono [rule_format (no_asm)]: "m <= n --> f(m) <= f(n)" |
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apply (induct_tac "n") |
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apply simp |
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apply (rule impI) |
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apply (erule le_SucE) |
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apply (cut_tac n = n in lemma2, auto) |
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done |
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lemma f_id: "f(n) = n" |
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apply (rule order_antisym) |
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apply (rule_tac [2] lemma1) |
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apply (blast intro: leI dest: leD f_mono Suc_leI) |
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done |
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end |
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