| author | wenzelm |
| Sat, 09 Jul 2011 21:53:27 +0200 | |
| changeset 43721 | fad8634cee62 |
| parent 41777 | 1f7cbe39d425 |
| child 58889 | 5b7a9633cfa8 |
| permissions | -rw-r--r-- |
| 41777 | 1 |
(* Title: FOL/ex/If.thy |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1991 University of Cambridge |
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*) |
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header {* First-Order Logic: the 'if' example *}
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theory If imports FOL begin |
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35416
d8d7d1b785af
replaced a couple of constsdefs by definitions (also some old primrecs by modern ones)
haftmann
parents:
31974
diff
changeset
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definition "if" :: "[o,o,o]=>o" where |
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"if(P,Q,R) == P&Q | ~P&R" |
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lemma ifI: |
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"[| P ==> Q; ~P ==> R |] ==> if(P,Q,R)" |
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apply (simp add: if_def, blast) |
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done |
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lemma ifE: |
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"[| if(P,Q,R); [| P; Q |] ==> S; [| ~P; R |] ==> S |] ==> S" |
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apply (simp add: if_def, blast) |
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done |
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lemma if_commute: "if(P, if(Q,A,B), if(Q,C,D)) <-> if(Q, if(P,A,C), if(P,B,D))" |
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apply (rule iffI) |
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apply (erule ifE) |
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apply (erule ifE) |
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apply (rule ifI) |
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apply (rule ifI) |
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oops |
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text{*Trying again from the beginning in order to use @{text blast}*}
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declare ifI [intro!] |
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declare ifE [elim!] |
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lemma if_commute: "if(P, if(Q,A,B), if(Q,C,D)) <-> if(Q, if(P,A,C), if(P,B,D))" |
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by blast |
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lemma "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,A,B))" |
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by blast |
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text{*Trying again from the beginning in order to prove from the definitions*}
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lemma "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,A,B))" |
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by (simp add: if_def, blast) |
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text{*An invalid formula. High-level rules permit a simpler diagnosis*}
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lemma "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,B,A))" |
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apply auto |
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-- {*The next step will fail unless subgoals remain*}
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apply (tactic all_tac) |
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oops |
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text{*Trying again from the beginning in order to prove from the definitions*}
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lemma "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,B,A))" |
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apply (simp add: if_def, auto) |
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-- {*The next step will fail unless subgoals remain*}
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apply (tactic all_tac) |
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oops |
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end |