| author | wenzelm |
| Mon, 07 Jan 2002 23:57:14 +0100 | |
| changeset 12659 | 2aa05eb15bd2 |
| parent 243 | c22b85994e17 |
| permissions | -rw-r--r-- |
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(* Title: HOLCF/sprod2.ML |
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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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Lemmas for sprod2.thy |
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*) |
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open Sprod2; |
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(* ------------------------------------------------------------------------ *) |
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(* access to less_sprod in class po *) |
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(* ------------------------------------------------------------------------ *) |
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val less_sprod3a = prove_goal Sprod2.thy |
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"p1=Ispair(UU,UU) ==> p1 << p2" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac (inst_sprod_po RS ssubst) 1), |
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(etac less_sprod1a 1) |
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]); |
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val less_sprod3b = prove_goal Sprod2.thy |
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"~p1=Ispair(UU,UU) ==>\ |
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\ (p1<<p2) = (Isfst(p1)<<Isfst(p2) & Issnd(p1)<<Issnd(p2))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac (inst_sprod_po RS ssubst) 1), |
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(etac less_sprod1b 1) |
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]); |
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val less_sprod4b = prove_goal Sprod2.thy |
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"p << Ispair(UU,UU) ==> p = 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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(rtac less_sprod2b 1), |
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(etac (inst_sprod_po RS subst) 1) |
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]); |
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val less_sprod4a = (less_sprod4b RS defined_Ispair_rev); |
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(* Ispair(?a,?b) << Ispair(UU,UU) ==> ?a = UU | ?b = UU *) |
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val less_sprod4c = prove_goal Sprod2.thy |
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"[|Ispair(xa,ya)<<Ispair(x,y);~xa=UU;~ya=UU;~x=UU;~y=UU|] ==>\ |
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\ xa<<x & ya << y" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac less_sprod2c 1), |
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(etac (inst_sprod_po RS subst) 1), |
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(REPEAT (atac 1)) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* type sprod is pointed *) |
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(* ------------------------------------------------------------------------ *) |
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val minimal_sprod = prove_goal Sprod2.thy "Ispair(UU,UU)<<p" |
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(fn prems => |
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[ |
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(rtac less_sprod3a 1), |
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(rtac refl 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* Ispair is monotone in both arguments *) |
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(* ------------------------------------------------------------------------ *) |
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val monofun_Ispair1 = prove_goalw Sprod2.thy [monofun] "monofun(Ispair)" |
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(fn prems => |
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[ |
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(strip_tac 1), |
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(rtac (less_fun RS iffD2) 1), |
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(strip_tac 1), |
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(res_inst_tac [("Q",
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" Ispair(y,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1), |
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(res_inst_tac [("Q",
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" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1), |
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(rtac (less_sprod3b RS iffD2) 1), |
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(atac 1), |
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(rtac conjI 1), |
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(rtac (Isfst RS ssubst) 1), |
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(etac (strict_Ispair_rev RS conjunct1) 1), |
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(etac (strict_Ispair_rev RS conjunct2) 1), |
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(rtac (Isfst RS ssubst) 1), |
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(etac (strict_Ispair_rev RS conjunct1) 1), |
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(etac (strict_Ispair_rev RS conjunct2) 1), |
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(atac 1), |
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(rtac (Issnd RS ssubst) 1), |
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(etac (strict_Ispair_rev RS conjunct1) 1), |
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(etac (strict_Ispair_rev RS conjunct2) 1), |
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(rtac (Issnd RS ssubst) 1), |
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(etac (strict_Ispair_rev RS conjunct1) 1), |
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(etac (strict_Ispair_rev RS conjunct2) 1), |
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(rtac refl_less 1), |
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(etac less_sprod3a 1), |
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(res_inst_tac [("Q",
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" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1), |
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(etac less_sprod3a 2), |
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(res_inst_tac [("P","Ispair(y,xa) = Ispair(UU,UU)")] notE 1),
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(atac 2), |
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(rtac defined_Ispair 1), |
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(etac notUU_I 1), |
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(etac (strict_Ispair_rev RS conjunct1) 1), |
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(etac (strict_Ispair_rev RS conjunct2) 1) |
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]); |
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val monofun_Ispair2 = prove_goalw Sprod2.thy [monofun] "monofun(Ispair(x))" |
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(fn prems => |
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[ |
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(strip_tac 1), |
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(res_inst_tac [("Q",
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" Ispair(x,y) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1), |
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(res_inst_tac [("Q",
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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121 |
" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
122 |
(rtac (less_sprod3b RS iffD2) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
123 |
(atac 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
124 |
(rtac conjI 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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changeset
|
125 |
(rtac (Isfst RS ssubst) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
126 |
(etac (strict_Ispair_rev RS conjunct1) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
127 |
(etac (strict_Ispair_rev RS conjunct2) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
128 |
(rtac (Isfst RS ssubst) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
129 |
(etac (strict_Ispair_rev RS conjunct1) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
130 |
(etac (strict_Ispair_rev RS conjunct2) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
131 |
(rtac refl_less 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
132 |
(rtac (Issnd RS ssubst) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
133 |
(etac (strict_Ispair_rev RS conjunct1) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
134 |
(etac (strict_Ispair_rev RS conjunct2) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
135 |
(rtac (Issnd RS ssubst) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
136 |
(etac (strict_Ispair_rev RS conjunct1) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
137 |
(etac (strict_Ispair_rev RS conjunct2) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
138 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
139 |
(etac less_sprod3a 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
140 |
(res_inst_tac [("Q",
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
141 |
" Ispair(x,xa) =Ispair(UU,UU)")] (excluded_middle RS disjE) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
142 |
(etac less_sprod3a 2), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
143 |
(res_inst_tac [("P","Ispair(x,y) = Ispair(UU,UU)")] notE 1),
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
144 |
(atac 2), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
145 |
(rtac defined_Ispair 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
146 |
(etac (strict_Ispair_rev RS conjunct1) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
147 |
(etac notUU_I 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
148 |
(etac (strict_Ispair_rev RS conjunct2) 1) |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
149 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
150 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
151 |
val monofun_Ispair = prove_goal Sprod2.thy |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
152 |
"[|x1<<x2; y1<<y2|] ==> Ispair(x1,y1)<<Ispair(x2,y2)" |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
153 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
154 |
[ |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
155 |
(cut_facts_tac prems 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
156 |
(rtac trans_less 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
157 |
(rtac (monofun_Ispair1 RS monofunE RS spec RS spec RS mp RS |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
158 |
(less_fun RS iffD1 RS spec)) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
159 |
(rtac (monofun_Ispair2 RS monofunE RS spec RS spec RS mp) 2), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
160 |
(atac 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
161 |
(atac 1) |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
162 |
]); |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
163 |
|
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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 |
(* ------------------------------------------------------------------------ *) |
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166 |
(* Isfst and Issnd are monotone *) |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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167 |
(* ------------------------------------------------------------------------ *) |
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|
168 |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
169 |
val monofun_Isfst = prove_goalw Sprod2.thy [monofun] "monofun(Isfst)" |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
170 |
(fn prems => |
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
171 |
[ |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
172 |
(strip_tac 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
173 |
(res_inst_tac [("p","x")] IsprodE 1),
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
174 |
(hyp_subst_tac 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
175 |
(rtac trans_less 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
176 |
(rtac minimal 2), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
177 |
(rtac (strict_Isfst1 RS ssubst) 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
178 |
(rtac refl_less 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
179 |
(hyp_subst_tac 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
180 |
(res_inst_tac [("p","y")] IsprodE 1),
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
181 |
(hyp_subst_tac 1), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
182 |
(res_inst_tac [("t","Isfst(Ispair(xa,ya))")] subst 1),
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
183 |
(rtac refl_less 2), |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
184 |
(etac (less_sprod4b RS sym RS arg_cong) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
185 |
(hyp_subst_tac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
186 |
(rtac (Isfst RS ssubst) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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changeset
|
187 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
188 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
189 |
(rtac (Isfst RS ssubst) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
190 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
191 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
192 |
(etac (less_sprod4c RS conjunct1) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
193 |
(REPEAT (atac 1)) |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
194 |
]); |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
195 |
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
196 |
val monofun_Issnd = prove_goalw Sprod2.thy [monofun] "monofun(Issnd)" |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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|
197 |
(fn prems => |
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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changeset
|
198 |
[ |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
199 |
(strip_tac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
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diff
changeset
|
200 |
(res_inst_tac [("p","x")] IsprodE 1),
|
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
201 |
(hyp_subst_tac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
202 |
(rtac trans_less 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
203 |
(rtac minimal 2), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
204 |
(rtac (strict_Issnd1 RS ssubst) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
205 |
(rtac refl_less 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
206 |
(hyp_subst_tac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
207 |
(res_inst_tac [("p","y")] IsprodE 1),
|
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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changeset
|
208 |
(hyp_subst_tac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
209 |
(res_inst_tac [("t","Issnd(Ispair(xa,ya))")] subst 1),
|
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
210 |
(rtac refl_less 2), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
211 |
(etac (less_sprod4b RS sym RS arg_cong) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
212 |
(hyp_subst_tac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
213 |
(rtac (Issnd RS ssubst) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
214 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
215 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
216 |
(rtac (Issnd RS ssubst) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
217 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
218 |
(atac 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
219 |
(etac (less_sprod4c RS conjunct2) 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
220 |
(REPEAT (atac 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
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changeset
|
223 |
|
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c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
224 |
(* ------------------------------------------------------------------------ *) |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
225 |
(* the type 'a ** 'b is a cpo *) |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
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|
226 |
(* ------------------------------------------------------------------------ *) |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
227 |
|
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
228 |
val lub_sprod = prove_goal Sprod2.thy |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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parents:
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|
229 |
"[|is_chain(S)|] ==> range(S) <<| \ |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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|
230 |
\ Ispair(lub(range(%i.Isfst(S(i)))),lub(range(%i.Issnd(S(i)))))" |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
231 |
(fn prems => |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
232 |
[ |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
233 |
(cut_facts_tac prems 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
234 |
(rtac is_lubI 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
235 |
(rtac conjI 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
236 |
(rtac ub_rangeI 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
237 |
(rtac allI 1), |
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
238 |
(res_inst_tac [("t","S(i)")] (surjective_pairing_Sprod RS ssubst) 1),
|
|
c22b85994e17
Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
nipkow
parents:
diff
changeset
|
239 |
(rtac monofun_Ispair 1), |
|
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Franz Regensburger's Higher-Order Logic of Computable Functions embedding LCF
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(rtac is_ub_thelub 1), |
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(etac (monofun_Isfst RS ch2ch_monofun) 1), |
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(rtac is_ub_thelub 1), |
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(etac (monofun_Issnd RS ch2ch_monofun) 1), |
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(strip_tac 1), |
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(res_inst_tac [("t","u")] (surjective_pairing_Sprod RS ssubst) 1),
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(rtac monofun_Ispair 1), |
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(rtac is_lub_thelub 1), |
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(etac (monofun_Isfst RS ch2ch_monofun) 1), |
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(etac (monofun_Isfst RS ub2ub_monofun) 1), |
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(rtac is_lub_thelub 1), |
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(etac (monofun_Issnd RS ch2ch_monofun) 1), |
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(etac (monofun_Issnd RS ub2ub_monofun) 1) |
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]); |
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val thelub_sprod = (lub_sprod RS thelubI); |
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(* is_chain(?S1) ==> lub(range(?S1)) = *) |
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(* Ispair(lub(range(%i. Isfst(?S1(i)))),lub(range(%i. Issnd(?S1(i))))) *) |
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val cpo_sprod = prove_goal Sprod2.thy |
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"is_chain(S::nat=>'a**'b)==>? x.range(S)<<| x" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac exI 1), |
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(etac lub_sprod 1) |
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]); |
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