author | clasohm |
Tue, 24 Oct 1995 14:45:35 +0100 | |
changeset 1294 | 1358dc040edb |
parent 1277 | caef3601c0b2 |
child 1461 | 6bcb44e4d6e5 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/sprod0.thy |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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|
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Lemmas for theory sprod0.thy |
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*) |
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|
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open Sprod0; |
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|
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(* ------------------------------------------------------------------------ *) |
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(* A non-emptyness result for Sprod *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "SprodI" Sprod0.thy [Sprod_def] |
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"(Spair_Rep a b):Sprod" |
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(fn prems => |
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[ |
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(EVERY1 [rtac CollectI, rtac exI,rtac exI, rtac refl]) |
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]); |
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qed_goal "inj_onto_Abs_Sprod" Sprod0.thy |
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"inj_onto Abs_Sprod Sprod" |
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(fn prems => |
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[ |
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(rtac inj_onto_inverseI 1), |
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(etac Abs_Sprod_inverse 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* Strictness and definedness of Spair_Rep *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "strict_Spair_Rep" Sprod0.thy [Spair_Rep_def] |
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"(a=UU | b=UU) ==> (Spair_Rep a b) = (Spair_Rep UU UU)" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac ext 1), |
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(rtac ext 1), |
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(rtac iffI 1), |
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(fast_tac HOL_cs 1), |
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(fast_tac HOL_cs 1) |
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]); |
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qed_goalw "defined_Spair_Rep_rev" Sprod0.thy [Spair_Rep_def] |
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"(Spair_Rep a b) = (Spair_Rep UU UU) ==> (a=UU | b=UU)" |
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(fn prems => |
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[ |
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(res_inst_tac [("Q","a=UU|b=UU")] classical2 1), |
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(atac 1), |
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(rtac disjI1 1), |
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(rtac ((hd prems) RS fun_cong RS fun_cong RS iffD2 RS mp RS |
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conjunct1 RS sym) 1), |
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(fast_tac HOL_cs 1), |
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(fast_tac HOL_cs 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* injectivity of Spair_Rep and Ispair *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "inject_Spair_Rep" Sprod0.thy [Spair_Rep_def] |
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"[|~aa=UU ; ~ba=UU ; Spair_Rep a b = Spair_Rep aa ba |] ==> a=aa & b=ba" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac ((nth_elem (2,prems)) RS fun_cong RS fun_cong |
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RS iffD1 RS mp) 1), |
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(fast_tac HOL_cs 1), |
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(fast_tac HOL_cs 1) |
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]); |
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qed_goalw "inject_Ispair" Sprod0.thy [Ispair_def] |
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"[|~aa=UU ; ~ba=UU ; Ispair a b = Ispair aa ba |] ==> a=aa & b=ba" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(etac inject_Spair_Rep 1), |
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(atac 1), |
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(etac (inj_onto_Abs_Sprod RS inj_ontoD) 1), |
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(rtac SprodI 1), |
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(rtac SprodI 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* strictness and definedness of Ispair *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "strict_Ispair" Sprod0.thy [Ispair_def] |
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"(a=UU | b=UU) ==> Ispair a b = Ispair UU UU" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(etac (strict_Spair_Rep RS arg_cong) 1) |
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qed_goalw "strict_Ispair1" Sprod0.thy [Ispair_def] |
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"Ispair UU b = Ispair UU UU" |
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(fn prems => |
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[ |
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(rtac (strict_Spair_Rep RS arg_cong) 1), |
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(rtac disjI1 1), |
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(rtac refl 1) |
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qed_goalw "strict_Ispair2" Sprod0.thy [Ispair_def] |
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"Ispair a UU = Ispair UU UU" |
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(fn prems => |
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[ |
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(rtac (strict_Spair_Rep RS arg_cong) 1), |
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(rtac disjI2 1), |
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(rtac refl 1) |
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]); |
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qed_goal "strict_Ispair_rev" Sprod0.thy |
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"~Ispair x y = Ispair UU UU ==> ~x=UU & ~y=UU" |
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[ |
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(cut_facts_tac prems 1), |
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(rtac (de_morgan1 RS ssubst) 1), |
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(etac contrapos 1), |
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(etac strict_Ispair 1) |
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]); |
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qed_goalw "defined_Ispair_rev" Sprod0.thy [Ispair_def] |
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"Ispair a b = Ispair UU UU ==> (a = UU | b = UU)" |
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[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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136 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
137 |
(rtac defined_Spair_Rep_rev 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
138 |
(rtac (inj_onto_Abs_Sprod RS inj_ontoD) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
139 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
140 |
(rtac SprodI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
141 |
(rtac SprodI 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
142 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
143 |
|
892 | 144 |
qed_goal "defined_Ispair" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
145 |
"[|a~=UU; b~=UU|] ==> (Ispair a b) ~= (Ispair UU UU)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
146 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
147 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
148 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
149 |
(rtac contrapos 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
150 |
(etac defined_Ispair_rev 2), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
151 |
(rtac (de_morgan1 RS iffD1) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
152 |
(etac conjI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
153 |
(atac 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
154 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
155 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
156 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
157 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
158 |
(* Exhaustion of the strict product ** *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
159 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
160 |
|
892 | 161 |
qed_goalw "Exh_Sprod" Sprod0.thy [Ispair_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
162 |
"z=Ispair UU UU | (? a b. z=Ispair a b & a~=UU & b~=UU)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
163 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
164 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
165 |
(rtac (rewrite_rule [Sprod_def] Rep_Sprod RS CollectE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
166 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
167 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
168 |
(rtac (excluded_middle RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
169 |
(rtac disjI2 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
170 |
(rtac exI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
171 |
(rtac exI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
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|
172 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
173 |
(rtac (Rep_Sprod_inverse RS sym RS trans) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
174 |
(etac arg_cong 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
175 |
(rtac (de_morgan1 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
176 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
177 |
(rtac disjI1 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
178 |
(rtac (Rep_Sprod_inverse RS sym RS trans) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
179 |
(res_inst_tac [("f","Abs_Sprod")] arg_cong 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
180 |
(etac trans 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
181 |
(etac strict_Spair_Rep 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
182 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
183 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
184 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
185 |
(* general elimination rule for strict product *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
186 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
187 |
|
892 | 188 |
qed_goal "IsprodE" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
189 |
"[|p=Ispair UU UU ==> Q ;!!x y. [|p=Ispair x y; x~=UU ; y~=UU|] ==> Q|] ==> Q" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
190 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
191 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
192 |
(rtac (Exh_Sprod RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
193 |
(etac (hd prems) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
194 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
195 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
196 |
(etac conjE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
197 |
(etac conjE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
198 |
(etac (hd (tl prems)) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
199 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
200 |
(atac 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
201 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
202 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
203 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
204 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
205 |
(* some results about the selectors Isfst, Issnd *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
206 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
207 |
|
892 | 208 |
qed_goalw "strict_Isfst" Sprod0.thy [Isfst_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
209 |
"p=Ispair UU UU ==> Isfst p = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
210 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
211 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
212 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
213 |
(rtac select_equality 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
214 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
215 |
(fast_tac HOL_cs 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
216 |
(strip_tac 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
217 |
(res_inst_tac [("P","Ispair UU UU = Ispair a b")] notE 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
218 |
(rtac not_sym 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
219 |
(rtac defined_Ispair 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
220 |
(REPEAT (fast_tac HOL_cs 1)) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
221 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
222 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
223 |
|
892 | 224 |
qed_goal "strict_Isfst1" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
225 |
"Isfst(Ispair UU y) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
226 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
227 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
228 |
(rtac (strict_Ispair1 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
229 |
(rtac strict_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
230 |
(rtac refl 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
231 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
232 |
|
892 | 233 |
qed_goal "strict_Isfst2" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
234 |
"Isfst(Ispair x UU) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
235 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
236 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
237 |
(rtac (strict_Ispair2 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
238 |
(rtac strict_Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
239 |
(rtac refl 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
240 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
241 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
242 |
|
892 | 243 |
qed_goalw "strict_Issnd" Sprod0.thy [Issnd_def] |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
244 |
"p=Ispair UU UU ==>Issnd p=UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
245 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
246 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
247 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
248 |
(rtac select_equality 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
249 |
(rtac conjI 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
250 |
(fast_tac HOL_cs 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
251 |
(strip_tac 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
252 |
(res_inst_tac [("P","Ispair UU UU = Ispair a b")] notE 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
253 |
(rtac not_sym 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
254 |
(rtac defined_Ispair 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
255 |
(REPEAT (fast_tac HOL_cs 1)) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
256 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
257 |
|
892 | 258 |
qed_goal "strict_Issnd1" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
259 |
"Issnd(Ispair UU y) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
260 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
261 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
262 |
(rtac (strict_Ispair1 RS ssubst) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
263 |
(rtac strict_Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
264 |
(rtac refl 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
265 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
266 |
|
892 | 267 |
qed_goal "strict_Issnd2" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
268 |
"Issnd(Ispair x UU) = UU" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
269 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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270 |
[ |
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271 |
(rtac (strict_Ispair2 RS ssubst) 1), |
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272 |
(rtac strict_Issnd 1), |
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|
273 |
(rtac refl 1) |
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274 |
]); |
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275 |
|
892 | 276 |
qed_goalw "Isfst" Sprod0.thy [Isfst_def] |
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|
277 |
"[|x~=UU ;y~=UU |] ==> Isfst(Ispair x y) = x" |
243
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278 |
(fn prems => |
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279 |
[ |
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280 |
(cut_facts_tac prems 1), |
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281 |
(rtac select_equality 1), |
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282 |
(rtac conjI 1), |
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|
283 |
(strip_tac 1), |
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74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
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|
284 |
(res_inst_tac [("P","Ispair x y = Ispair UU UU")] notE 1), |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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285 |
(etac defined_Ispair 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
286 |
(atac 1), |
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|
287 |
(atac 1), |
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|
288 |
(strip_tac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
289 |
(rtac (inject_Ispair RS conjunct1) 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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290 |
(fast_tac HOL_cs 3), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
291 |
(fast_tac HOL_cs 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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292 |
(fast_tac HOL_cs 1), |
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293 |
(fast_tac HOL_cs 1) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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294 |
]); |
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295 |
|
892 | 296 |
qed_goalw "Issnd" Sprod0.thy [Issnd_def] |
1168
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regensbu
parents:
892
diff
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|
297 |
"[|x~=UU ;y~=UU |] ==> Issnd(Ispair x y) = y" |
243
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|
298 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
299 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
300 |
(cut_facts_tac prems 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
301 |
(rtac select_equality 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
302 |
(rtac conjI 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
303 |
(strip_tac 1), |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
304 |
(res_inst_tac [("P","Ispair x y = Ispair UU UU")] notE 1), |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
305 |
(etac defined_Ispair 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
306 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
307 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
308 |
(strip_tac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
309 |
(rtac (inject_Ispair RS conjunct2) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
310 |
(fast_tac HOL_cs 3), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
311 |
(fast_tac HOL_cs 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
312 |
(fast_tac HOL_cs 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
313 |
(fast_tac HOL_cs 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
314 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
315 |
|
1168
74be52691d62
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regensbu
parents:
892
diff
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|
316 |
qed_goal "Isfst2" Sprod0.thy "y~=UU ==>Isfst(Ispair x y)=x" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
317 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
318 |
[ |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
319 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
changeset
|
320 |
(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
321 |
(etac Isfst 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
322 |
(atac 1), |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
323 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
324 |
(rtac strict_Isfst1 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
325 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
diff
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|
326 |
|
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
327 |
qed_goal "Issnd2" Sprod0.thy "~x=UU ==>Issnd(Ispair x y)=y" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
328 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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diff
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|
329 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
330 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
331 |
(res_inst_tac [("Q","y=UU")] (excluded_middle RS disjE) 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
332 |
(etac Issnd 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
333 |
(atac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
334 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
335 |
(rtac strict_Issnd2 1) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
336 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
337 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
338 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
339 |
(* ------------------------------------------------------------------------ *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
340 |
(* instantiate the simplifier *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
341 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
342 |
|
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
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|
343 |
val Sprod0_ss = |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
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diff
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|
344 |
HOL_ss |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
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|
345 |
addsimps [strict_Isfst1,strict_Isfst2,strict_Issnd1,strict_Issnd2, |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
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|
346 |
Isfst2,Issnd2]; |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
347 |
|
892 | 348 |
qed_goal "defined_IsfstIssnd" Sprod0.thy |
1168
74be52691d62
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regensbu
parents:
892
diff
changeset
|
349 |
"p~=Ispair UU UU ==> Isfst p ~= UU & Issnd p ~= UU" |
243
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
350 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
351 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
352 |
(cut_facts_tac prems 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
353 |
(res_inst_tac [("p","p")] IsprodE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
354 |
(contr_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
355 |
(hyp_subst_tac 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
356 |
(rtac conjI 1), |
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
changeset
|
357 |
(asm_simp_tac Sprod0_ss 1), |
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
changeset
|
358 |
(asm_simp_tac Sprod0_ss 1) |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
359 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
360 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
361 |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
362 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
363 |
(* Surjective pairing: equivalent to Exh_Sprod *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
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|
364 |
(* ------------------------------------------------------------------------ *) |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
365 |
|
892 | 366 |
qed_goal "surjective_pairing_Sprod" Sprod0.thy |
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
892
diff
changeset
|
367 |
"z = Ispair(Isfst z)(Issnd z)" |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
368 |
(fn prems => |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
369 |
[ |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
370 |
(res_inst_tac [("z1","z")] (Exh_Sprod RS disjE) 1), |
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
changeset
|
371 |
(asm_simp_tac Sprod0_ss 1), |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
372 |
(etac exE 1), |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
373 |
(etac exE 1), |
1277
caef3601c0b2
corrected some errors that occurred after introduction of local simpsets
regensbu
parents:
1274
diff
changeset
|
374 |
(asm_simp_tac Sprod0_ss 1) |
243
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
375 |
]); |
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
376 |