author | oheimb |
Fri, 01 May 1998 22:30:42 +0200 | |
changeset 4884 | 1ec740e30811 |
parent 4883 | c1aec06d1dca |
child 4926 | 0fd0b3f3bc25 |
permissions | -rw-r--r-- |
3981 | 1 |
(* Title: HOL/Map.ML |
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ID: $Id$ |
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Author: Tobias Nipkow |
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Copyright 1997 TU Muenchen |
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Map lemmas |
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*) |
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goalw thy [empty_def] "empty k = None"; |
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by (Simp_tac 1); |
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qed "empty_def2"; |
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Addsimps [empty_def2]; |
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goalw thy [update_def] "(m[a|->b])x = (if x=a then Some b else m x)"; |
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by (Simp_tac 1); |
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qed "update_def2"; |
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Addsimps [update_def2]; |
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4526
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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qed_goal "update_same" thy "(t[k|->x]) k = Some x" |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
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(K [Simp_tac 1]); |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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qed_goal "update_other" thy "!!X. l~=k ==> (t[k|->x]) l = t l" |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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(K [Asm_simp_tac 1]); |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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qed_goal "update_triv" thy "!!X. t k = Some x ==> t[k|->x] = t" |
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(K [rtac ext 1, Asm_simp_tac 1]); |
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6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
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diff
changeset
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(*Addsimps [update_same, update_other, update_triv];*) |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
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diff
changeset
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section "++"; |
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goalw thy [override_def] "m ++ empty = m"; |
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by (Simp_tac 1); |
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qed "override_empty"; |
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Addsimps [override_empty]; |
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goalw thy [override_def] "empty ++ m = m"; |
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by (Simp_tac 1); |
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by (rtac ext 1); |
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by (split_tac [split_option_case] 1); |
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by (Simp_tac 1); |
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qed "empty_override"; |
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Addsimps [empty_override]; |
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goalw thy [override_def] |
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"((m ++ n) k = Some x) = (n k = Some x | n k = None & m k = Some x)"; |
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by (simp_tac (simpset() addsplits [split_option_case]) 1); |
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qed_spec_mp "override_Some_iff"; |
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bind_thm("override_SomeD", standard(override_Some_iff RS iffD1)); |
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goalw thy [override_def] |
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"((m ++ n) k = None) = (n k = None & m k = None)"; |
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by (simp_tac (simpset() addsplits [split_option_case]) 1); |
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qed "override_None"; |
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AddIffs [override_None]; |
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goalw thy [override_def] "map_of(xs@ys) = map_of ys ++ map_of xs"; |
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by (induct_tac "xs" 1); |
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by (Simp_tac 1); |
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by (rtac ext 1); |
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by (asm_simp_tac (simpset() addsplits [split_option_case]) 1); |
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qed "map_of_append"; |
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Addsimps [map_of_append]; |
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6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
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goal thy "map_of xs k = Some y --> (k,y):set xs"; |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
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parents:
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by (list.induct_tac "xs" 1); |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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by (Simp_tac 1); |
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by (split_all_tac 1); |
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by (Asm_simp_tac 1); |
4526
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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qed_spec_mp "map_of_SomeD"; |
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
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section "dom"; |
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goalw thy [dom_def] "dom empty = {}"; |
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by (Simp_tac 1); |
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qed "dom_empty"; |
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Addsimps [dom_empty]; |
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goalw thy [dom_def] "dom(m[a|->b]) = insert a (dom m)"; |
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by (Simp_tac 1); |
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by (Blast_tac 1); |
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qed "dom_update"; |
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Addsimps [dom_update]; |
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qed_goalw "finite_dom_map_of" Map.thy [dom_def] "finite (dom (map_of l))" (K[ |
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list.induct_tac "l" 1, |
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ALLGOALS Simp_tac, |
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stac (insert_Collect RS sym) 1, |
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Asm_simp_tac 1]); |
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goalw thy [dom_def] "dom(m++n) = dom n Un dom m"; |
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by (Blast_tac 1); |
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qed "dom_override"; |
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Addsimps [dom_override]; |
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section "ran"; |
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goalw thy [ran_def] "ran empty = {}"; |
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by (Simp_tac 1); |
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qed "ran_empty"; |
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Addsimps [ran_empty]; |
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goalw thy [ran_def] "!!X. m a = None ==> ran(m[a|->b]) = insert b (ran m)"; |
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by Auto_tac; |
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by (subgoal_tac "~(aa = a)" 1); |
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by Auto_tac; |
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qed "ran_update"; |
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Addsimps [ran_update]; |