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(* Title: HOLCF/dlist.ML
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Author: Franz Regensburger
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ID: $ $
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Copyright 1994 Technische Universitaet Muenchen
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Lemmas for dlist.thy
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*)
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open Dlist;
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(* ------------------------------------------------------------------------*)
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(* The isomorphisms dlist_rep_iso and dlist_abs_iso are strict *)
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(* ------------------------------------------------------------------------*)
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val dlist_iso_strict= dlist_rep_iso RS (dlist_abs_iso RS
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(allI RSN (2,allI RS iso_strict)));
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val dlist_rews = [dlist_iso_strict RS conjunct1,
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dlist_iso_strict RS conjunct2];
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(* ------------------------------------------------------------------------*)
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(* Properties of dlist_copy *)
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(* ------------------------------------------------------------------------*)
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val temp = prove_goalw Dlist.thy [dlist_copy_def] "dlist_copy[f][UU]=UU"
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(fn prems =>
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[
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(asm_simp_tac (HOLCF_ss addsimps
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(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1)
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]);
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val dlist_copy = [temp];
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val temp = prove_goalw Dlist.thy [dlist_copy_def,dnil_def]
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"dlist_copy[f][dnil]=dnil"
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(fn prems =>
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[
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(asm_simp_tac (HOLCF_ss addsimps
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(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1)
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]);
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val dlist_copy = temp :: dlist_copy;
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val temp = prove_goalw Dlist.thy [dlist_copy_def,dcons_def]
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"xl~=UU ==> dlist_copy[f][dcons[x][xl]]= dcons[x][f[xl]]"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(asm_simp_tac (HOLCF_ss addsimps
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(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1),
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(res_inst_tac [("Q","x=UU")] classical2 1),
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(asm_simp_tac HOLCF_ss 1),
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(asm_simp_tac (HOLCF_ss addsimps [defined_spair]) 1)
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]);
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val dlist_copy = temp :: dlist_copy;
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val dlist_rews = dlist_copy @ dlist_rews;
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(* ------------------------------------------------------------------------*)
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(* Exhaustion and elimination for dlists *)
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(* ------------------------------------------------------------------------*)
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val Exh_dlist = prove_goalw Dlist.thy [dcons_def,dnil_def]
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"l = UU | l = dnil | (? x xl. x~=UU &xl~=UU & l = dcons[x][xl])"
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(fn prems =>
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[
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(simp_tac HOLCF_ss 1),
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(rtac (dlist_rep_iso RS subst) 1),
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(res_inst_tac [("p","dlist_rep[l]")] ssumE 1),
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(rtac disjI1 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(rtac disjI2 1),
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(rtac disjI1 1),
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(res_inst_tac [("p","x")] oneE 1),
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(contr_tac 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(rtac disjI2 1),
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(rtac disjI2 1),
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(res_inst_tac [("p","y")] sprodE 1),
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(contr_tac 1),
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(rtac exI 1),
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(rtac exI 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(fast_tac HOL_cs 1)
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]);
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val dlistE = prove_goal Dlist.thy
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"[| l=UU ==> Q; l=dnil ==> Q;!!x xl.[|l=dcons[x][xl];x~=UU;xl~=UU|]==>Q|]==>Q"
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(fn prems =>
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[
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(rtac (Exh_dlist RS disjE) 1),
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(eresolve_tac prems 1),
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(etac disjE 1),
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(eresolve_tac prems 1),
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(etac exE 1),
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(etac exE 1),
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(resolve_tac prems 1),
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(fast_tac HOL_cs 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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(* Properties of dlist_when *)
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(* ------------------------------------------------------------------------*)
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val temp = prove_goalw Dlist.thy [dlist_when_def] "dlist_when[f1][f2][UU]=UU"
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(fn prems =>
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[
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(asm_simp_tac (HOLCF_ss addsimps [dlist_iso_strict]) 1)
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]);
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val dlist_when = [temp];
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val temp = prove_goalw Dlist.thy [dlist_when_def,dnil_def]
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"dlist_when[f1][f2][dnil]= f1"
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(fn prems =>
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[
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(asm_simp_tac (HOLCF_ss addsimps [dlist_abs_iso]) 1)
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]);
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val dlist_when = temp::dlist_when;
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val temp = prove_goalw Dlist.thy [dlist_when_def,dcons_def]
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"[|x~=UU;xl~=UU|] ==> dlist_when[f1][f2][dcons[x][xl]]= f2[x][xl]"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(asm_simp_tac (HOLCF_ss addsimps [dlist_abs_iso,defined_spair]) 1)
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]);
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val dlist_when = temp::dlist_when;
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val dlist_rews = dlist_when @ dlist_rews;
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(* ------------------------------------------------------------------------*)
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(* Rewrites for discriminators and selectors *)
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(* ------------------------------------------------------------------------*)
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fun prover defs thm = prove_goalw Dlist.thy defs thm
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(fn prems =>
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[
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(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dlist_discsel = [
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prover [is_dnil_def] "is_dnil[UU]=UU",
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prover [is_dcons_def] "is_dcons[UU]=UU",
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prover [dhd_def] "dhd[UU]=UU",
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prover [dtl_def] "dtl[UU]=UU"
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];
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fun prover defs thm = prove_goalw Dlist.thy defs thm
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dlist_discsel = [
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"is_dnil[dnil]=TT",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"[|x~=UU;xl~=UU|] ==> is_dnil[dcons[x][xl]]=FF",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"is_dcons[dnil]=FF",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"[|x~=UU;xl~=UU|] ==> is_dcons[dcons[x][xl]]=TT",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"dhd[dnil]=UU",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"[|x~=UU;xl~=UU|] ==> dhd[dcons[x][xl]]=x",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"dtl[dnil]=UU",
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prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
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"[|x~=UU;xl~=UU|] ==> dtl[dcons[x][xl]]=xl"] @ dlist_discsel;
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val dlist_rews = dlist_discsel @ dlist_rews;
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(* ------------------------------------------------------------------------*)
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(* Definedness and strictness *)
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(* ------------------------------------------------------------------------*)
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fun prover contr thm = prove_goal Dlist.thy thm
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(fn prems =>
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[
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(res_inst_tac [("P1",contr)] classical3 1),
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(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(dtac sym 1),
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(asm_simp_tac HOLCF_ss 1),
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(simp_tac (HOLCF_ss addsimps (prems @ dlist_rews)) 1)
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]);
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val dlist_constrdef = [
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prover "is_dnil[UU] ~= UU" "dnil~=UU",
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prover "is_dcons[UU] ~= UU" "[|x~=UU;xl~=UU|] ==> dcons[x][xl]~=UU"
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];
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fun prover defs thm = prove_goalw Dlist.thy defs thm
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(fn prems =>
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[
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(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dlist_constrdef = [
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prover [dcons_def] "dcons[UU][xl]=UU",
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prover [dcons_def] "dcons[x][UU]=UU"
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] @ dlist_constrdef;
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val dlist_rews = dlist_constrdef @ dlist_rews;
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(* ------------------------------------------------------------------------*)
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(* Distinctness wrt. << and = *)
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(* ------------------------------------------------------------------------*)
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val temp = prove_goal Dlist.thy "~dnil << dcons[x][xl]"
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(fn prems =>
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[
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(res_inst_tac [("P1","TT << FF")] classical3 1),
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(resolve_tac dist_less_tr 1),
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(dres_inst_tac [("fo5","is_dnil")] monofun_cfun_arg 1),
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(etac box_less 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(res_inst_tac [("Q","x=UU")] classical2 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(res_inst_tac [("Q","xl=UU")] classical2 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dlist_dist_less = [temp];
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val temp = prove_goal Dlist.thy "[|x~=UU;xl~=UU|]==>~dcons[x][xl] << dnil"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(res_inst_tac [("P1","TT << FF")] classical3 1),
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(resolve_tac dist_less_tr 1),
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(dres_inst_tac [("fo5","is_dcons")] monofun_cfun_arg 1),
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(etac box_less 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dlist_dist_less = temp::dlist_dist_less;
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val temp = prove_goal Dlist.thy "dnil ~= dcons[x][xl]"
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(fn prems =>
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[
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(res_inst_tac [("Q","x=UU")] classical2 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(res_inst_tac [("Q","xl=UU")] classical2 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(res_inst_tac [("P1","TT = FF")] classical3 1),
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(resolve_tac dist_eq_tr 1),
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(dres_inst_tac [("f","is_dnil")] cfun_arg_cong 1),
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(etac box_equals 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dlist_dist_eq = [temp,temp RS not_sym];
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val dlist_rews = dlist_dist_less @ dlist_dist_eq @ dlist_rews;
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(* ------------------------------------------------------------------------*)
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(* Invertibility *)
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(* ------------------------------------------------------------------------*)
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val temp = prove_goal Dlist.thy "[|x1~=UU; y1~=UU;x2~=UU; y2~=UU;\
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\ dcons[x1][x2] << dcons[y1][y2]|] ==> x1<< y1 & x2 << y2"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(rtac conjI 1),
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(dres_inst_tac [("fo5","dlist_when[UU][LAM x l.x]")] monofun_cfun_arg 1),
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(etac box_less 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
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(dres_inst_tac [("fo5","dlist_when[UU][LAM x l.l]")] monofun_cfun_arg 1),
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(etac box_less 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1)
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]);
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val dlist_invert =[temp];
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(* ------------------------------------------------------------------------*)
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(* Injectivity *)
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(* ------------------------------------------------------------------------*)
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val temp = prove_goal Dlist.thy "[|x1~=UU; y1~=UU;x2~=UU; y2~=UU;\
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\ dcons[x1][x2] = dcons[y1][y2]|] ==> x1= y1 & x2 = y2"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(rtac conjI 1),
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(dres_inst_tac [("f","dlist_when[UU][LAM x l.x]")] cfun_arg_cong 1),
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(etac box_equals 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
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(dres_inst_tac [("f","dlist_when[UU][LAM x l.l]")] cfun_arg_cong 1),
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(etac box_equals 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1)
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]);
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val dlist_inject = [temp];
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(* ------------------------------------------------------------------------*)
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(* definedness for discriminators and selectors *)
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(* ------------------------------------------------------------------------*)
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fun prover thm = prove_goal Dlist.thy thm
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(rtac dlistE 1),
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(contr_tac 1),
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(REPEAT (asm_simp_tac (HOLCF_ss addsimps dlist_discsel) 1))
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]);
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val dlist_discsel_def =
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[
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prover "l~=UU ==> is_dnil[l]~=UU",
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prover "l~=UU ==> is_dcons[l]~=UU"
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];
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val dlist_rews = dlist_discsel_def @ dlist_rews;
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(* ------------------------------------------------------------------------*)
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(* enhance the simplifier *)
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(* ------------------------------------------------------------------------*)
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val dhd2 = prove_goal Dlist.thy "xl~=UU ==> dhd[dcons[x][xl]]=x"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(res_inst_tac [("Q","x=UU")] classical2 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
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]);
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val dtl2 = prove_goal Dlist.thy "x~=UU ==> dtl[dcons[x][xl]]=xl"
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(fn prems =>
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[
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(cut_facts_tac prems 1),
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(res_inst_tac [("Q","xl=UU")] classical2 1),
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(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
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358 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
|
|
359 |
]);
|
|
360 |
|
|
361 |
val dlist_rews = dhd2 :: dtl2 :: dlist_rews;
|
|
362 |
|
|
363 |
(* ------------------------------------------------------------------------*)
|
|
364 |
(* Properties dlist_take *)
|
|
365 |
(* ------------------------------------------------------------------------*)
|
|
366 |
|
|
367 |
val temp = prove_goalw Dlist.thy [dlist_take_def] "dlist_take(n)[UU]=UU"
|
|
368 |
(fn prems =>
|
|
369 |
[
|
|
370 |
(res_inst_tac [("n","n")] natE 1),
|
|
371 |
(asm_simp_tac iterate_ss 1),
|
|
372 |
(asm_simp_tac iterate_ss 1),
|
|
373 |
(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
|
|
374 |
]);
|
|
375 |
|
|
376 |
val dlist_take = [temp];
|
|
377 |
|
|
378 |
val temp = prove_goalw Dlist.thy [dlist_take_def] "dlist_take(0)[xs]=UU"
|
|
379 |
(fn prems =>
|
|
380 |
[
|
|
381 |
(asm_simp_tac iterate_ss 1)
|
|
382 |
]);
|
|
383 |
|
|
384 |
val dlist_take = temp::dlist_take;
|
|
385 |
|
|
386 |
val temp = prove_goalw Dlist.thy [dlist_take_def]
|
|
387 |
"dlist_take(Suc(n))[dnil]=dnil"
|
|
388 |
(fn prems =>
|
|
389 |
[
|
|
390 |
(asm_simp_tac iterate_ss 1),
|
|
391 |
(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
|
|
392 |
]);
|
|
393 |
|
|
394 |
val dlist_take = temp::dlist_take;
|
|
395 |
|
|
396 |
val temp = prove_goalw Dlist.thy [dlist_take_def]
|
|
397 |
"dlist_take(Suc(n))[dcons[x][xl]]=dcons[x][dlist_take(n)[xl]]"
|
|
398 |
(fn prems =>
|
|
399 |
[
|
|
400 |
(res_inst_tac [("Q","x=UU")] classical2 1),
|
|
401 |
(asm_simp_tac iterate_ss 1),
|
|
402 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
403 |
(res_inst_tac [("Q","xl=UU")] classical2 1),
|
|
404 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
405 |
(asm_simp_tac iterate_ss 1),
|
|
406 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
407 |
(res_inst_tac [("n","n")] natE 1),
|
|
408 |
(asm_simp_tac iterate_ss 1),
|
|
409 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
410 |
(asm_simp_tac iterate_ss 1),
|
|
411 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
412 |
(asm_simp_tac iterate_ss 1),
|
|
413 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
|
|
414 |
]);
|
|
415 |
|
|
416 |
val dlist_take = temp::dlist_take;
|
|
417 |
|
|
418 |
val dlist_rews = dlist_take @ dlist_rews;
|
|
419 |
|
|
420 |
(* ------------------------------------------------------------------------*)
|
|
421 |
(* take lemma for dlists *)
|
|
422 |
(* ------------------------------------------------------------------------*)
|
|
423 |
|
|
424 |
fun prover reach defs thm = prove_goalw Dlist.thy defs thm
|
|
425 |
(fn prems =>
|
|
426 |
[
|
|
427 |
(res_inst_tac [("t","l1")] (reach RS subst) 1),
|
|
428 |
(res_inst_tac [("t","l2")] (reach RS subst) 1),
|
|
429 |
(rtac (fix_def2 RS ssubst) 1),
|
|
430 |
(rtac (contlub_cfun_fun RS ssubst) 1),
|
|
431 |
(rtac is_chain_iterate 1),
|
|
432 |
(rtac (contlub_cfun_fun RS ssubst) 1),
|
|
433 |
(rtac is_chain_iterate 1),
|
|
434 |
(rtac lub_equal 1),
|
|
435 |
(rtac (is_chain_iterate RS ch2ch_fappL) 1),
|
|
436 |
(rtac (is_chain_iterate RS ch2ch_fappL) 1),
|
|
437 |
(rtac allI 1),
|
|
438 |
(resolve_tac prems 1)
|
|
439 |
]);
|
|
440 |
|
|
441 |
val dlist_take_lemma = prover dlist_reach [dlist_take_def]
|
|
442 |
"(!!n.dlist_take(n)[l1]=dlist_take(n)[l2]) ==> l1=l2";
|
|
443 |
|
|
444 |
|
|
445 |
(* ------------------------------------------------------------------------*)
|
|
446 |
(* Co -induction for dlists *)
|
|
447 |
(* ------------------------------------------------------------------------*)
|
|
448 |
|
|
449 |
val dlist_coind_lemma = prove_goalw Dlist.thy [dlist_bisim_def]
|
|
450 |
"dlist_bisim(R) ==> ! p q.R(p,q) --> dlist_take(n)[p]=dlist_take(n)[q]"
|
|
451 |
(fn prems =>
|
|
452 |
[
|
|
453 |
(cut_facts_tac prems 1),
|
|
454 |
(nat_ind_tac "n" 1),
|
|
455 |
(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
456 |
(strip_tac 1),
|
|
457 |
((etac allE 1) THEN (etac allE 1) THEN (etac (mp RS disjE) 1)),
|
|
458 |
(atac 1),
|
|
459 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
460 |
(etac disjE 1),
|
|
461 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
462 |
(etac exE 1),
|
|
463 |
(etac exE 1),
|
|
464 |
(etac exE 1),
|
|
465 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
466 |
(REPEAT (etac conjE 1)),
|
|
467 |
(rtac cfun_arg_cong 1),
|
|
468 |
(fast_tac HOL_cs 1)
|
|
469 |
]);
|
|
470 |
|
|
471 |
val dlist_coind = prove_goal Dlist.thy "[|dlist_bisim(R);R(p,q)|] ==> p = q"
|
|
472 |
(fn prems =>
|
|
473 |
[
|
|
474 |
(rtac dlist_take_lemma 1),
|
|
475 |
(rtac (dlist_coind_lemma RS spec RS spec RS mp) 1),
|
|
476 |
(resolve_tac prems 1),
|
|
477 |
(resolve_tac prems 1)
|
|
478 |
]);
|
|
479 |
|
|
480 |
(* ------------------------------------------------------------------------*)
|
|
481 |
(* structural induction *)
|
|
482 |
(* ------------------------------------------------------------------------*)
|
|
483 |
|
|
484 |
val dlist_finite_ind = prove_goal Dlist.thy
|
|
485 |
"[|P(UU);P(dnil);\
|
|
486 |
\ !! x l1.[|x~=UU;l1~=UU;P(l1)|] ==> P(dcons[x][l1])\
|
|
487 |
\ |] ==> !l.P(dlist_take(n)[l])"
|
|
488 |
(fn prems =>
|
|
489 |
[
|
|
490 |
(nat_ind_tac "n" 1),
|
|
491 |
(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
492 |
(resolve_tac prems 1),
|
|
493 |
(rtac allI 1),
|
|
494 |
(res_inst_tac [("l","l")] dlistE 1),
|
|
495 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
496 |
(resolve_tac prems 1),
|
|
497 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
498 |
(resolve_tac prems 1),
|
|
499 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
500 |
(res_inst_tac [("Q","dlist_take(n1)[xl]=UU")] classical2 1),
|
|
501 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
502 |
(resolve_tac prems 1),
|
|
503 |
(resolve_tac prems 1),
|
|
504 |
(atac 1),
|
|
505 |
(atac 1),
|
|
506 |
(etac spec 1)
|
|
507 |
]);
|
|
508 |
|
|
509 |
val dlist_all_finite_lemma1 = prove_goal Dlist.thy
|
|
510 |
"!l.dlist_take(n)[l]=UU |dlist_take(n)[l]=l"
|
|
511 |
(fn prems =>
|
|
512 |
[
|
|
513 |
(nat_ind_tac "n" 1),
|
|
514 |
(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
515 |
(rtac allI 1),
|
|
516 |
(res_inst_tac [("l","l")] dlistE 1),
|
|
517 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
518 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
519 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
520 |
(eres_inst_tac [("x","xl")] allE 1),
|
|
521 |
(etac disjE 1),
|
|
522 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
523 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
|
|
524 |
]);
|
|
525 |
|
|
526 |
val dlist_all_finite_lemma2 = prove_goal Dlist.thy "? n.dlist_take(n)[l]=l"
|
|
527 |
(fn prems =>
|
|
528 |
[
|
|
529 |
(res_inst_tac [("Q","l=UU")] classical2 1),
|
|
530 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
531 |
(subgoal_tac "(!n.dlist_take(n)[l]=UU) |(? n.dlist_take(n)[l]=l)" 1),
|
|
532 |
(etac disjE 1),
|
|
533 |
(eres_inst_tac [("P","l=UU")] notE 1),
|
|
534 |
(rtac dlist_take_lemma 1),
|
|
535 |
(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
|
|
536 |
(atac 1),
|
|
537 |
(subgoal_tac "!n.!l.dlist_take(n)[l]=UU |dlist_take(n)[l]=l" 1),
|
|
538 |
(fast_tac HOL_cs 1),
|
|
539 |
(rtac allI 1),
|
|
540 |
(rtac dlist_all_finite_lemma1 1)
|
|
541 |
]);
|
|
542 |
|
|
543 |
val dlist_all_finite= prove_goalw Dlist.thy [dlist_finite_def] "dlist_finite(l)"
|
|
544 |
(fn prems =>
|
|
545 |
[
|
|
546 |
(rtac dlist_all_finite_lemma2 1)
|
|
547 |
]);
|
|
548 |
|
|
549 |
val dlist_ind = prove_goal Dlist.thy
|
|
550 |
"[|P(UU);P(dnil);\
|
|
551 |
\ !! x l1.[|x~=UU;l1~=UU;P(l1)|] ==> P(dcons[x][l1])|] ==> P(l)"
|
|
552 |
(fn prems =>
|
|
553 |
[
|
|
554 |
(rtac (dlist_all_finite_lemma2 RS exE) 1),
|
|
555 |
(etac subst 1),
|
|
556 |
(rtac (dlist_finite_ind RS spec) 1),
|
|
557 |
(REPEAT (resolve_tac prems 1)),
|
|
558 |
(REPEAT (atac 1))
|
|
559 |
]);
|
|
560 |
|
|
561 |
|
|
562 |
|
|
563 |
|