src/HOLCF/Pcpo.ML
changeset 3726 2543df678ab2
parent 3326 930c9bed5a09
child 3842 b55686a7b22c
equal deleted inserted replaced
3725:c7fa890d0d92 3726:2543df678ab2
   119         (rtac ub_rangeI 1),
   119         (rtac ub_rangeI 1),
   120         (strip_tac 1),
   120         (strip_tac 1),
   121         (case_tac "x<i" 1),
   121         (case_tac "x<i" 1),
   122         (res_inst_tac [("s","Y(i)"),("t","X(i)")] subst 1),
   122         (res_inst_tac [("s","Y(i)"),("t","X(i)")] subst 1),
   123         (rtac sym 1),
   123         (rtac sym 1),
   124         (fast_tac HOL_cs 1),
   124         (Fast_tac 1),
   125         (rtac is_ub_thelub 1),
   125         (rtac is_ub_thelub 1),
   126         (resolve_tac prems 1),
   126         (resolve_tac prems 1),
   127         (res_inst_tac [("y","X(Suc(x))")] trans_less 1),
   127         (res_inst_tac [("y","X(Suc(x))")] trans_less 1),
   128         (rtac (chain_mono RS mp) 1),
   128         (rtac (chain_mono RS mp) 1),
   129         (resolve_tac prems 1),
   129         (resolve_tac prems 1),
   144         (rtac antisym_less 1),
   144         (rtac antisym_less 1),
   145         (rtac lub_mono2 1),
   145         (rtac lub_mono2 1),
   146         (REPEAT (resolve_tac prems 1)),
   146         (REPEAT (resolve_tac prems 1)),
   147         (cut_facts_tac prems 1),
   147         (cut_facts_tac prems 1),
   148         (rtac lub_mono2 1),
   148         (rtac lub_mono2 1),
   149         (safe_tac HOL_cs),
   149         Safe_tac,
   150         (step_tac HOL_cs 1),
   150         (Step_tac 1),
   151         (safe_tac HOL_cs),
   151         Safe_tac,
   152         (rtac sym 1),
   152         (rtac sym 1),
   153         (fast_tac HOL_cs 1)
   153         (Fast_tac 1)
   154         ]);
   154         ]);
   155 
   155 
   156 qed_goal "lub_mono3" thy "[|is_chain(Y::nat=>'a::cpo);is_chain(X);\
   156 qed_goal "lub_mono3" thy "[|is_chain(Y::nat=>'a::cpo);is_chain(X);\
   157 \! i. ? j. Y(i)<< X(j)|]==> lub(range(Y))<<lub(range(X))"
   157 \! i. ? j. Y(i)<< X(j)|]==> lub(range(Y))<<lub(range(X))"
   158  (fn prems =>
   158  (fn prems =>
   173 (* ------------------------------------------------------------------------ *)
   173 (* ------------------------------------------------------------------------ *)
   174 (* usefull lemmas about UU                                                  *)
   174 (* usefull lemmas about UU                                                  *)
   175 (* ------------------------------------------------------------------------ *)
   175 (* ------------------------------------------------------------------------ *)
   176 
   176 
   177 val eq_UU_sym = prove_goal thy "(UU = x) = (x = UU)" (fn _ => [
   177 val eq_UU_sym = prove_goal thy "(UU = x) = (x = UU)" (fn _ => [
   178         fast_tac HOL_cs 1]);
   178         Fast_tac 1]);
   179 
   179 
   180 qed_goal "eq_UU_iff" thy "(x=UU)=(x<<UU)"
   180 qed_goal "eq_UU_iff" thy "(x=UU)=(x<<UU)"
   181  (fn prems =>
   181  (fn prems =>
   182         [
   182         [
   183         (rtac iffI 1),
   183         (rtac iffI 1),
   259 "[|? j.~Y(j)=UU;is_chain(Y::nat=>'a::pcpo)|]\
   259 "[|? j.~Y(j)=UU;is_chain(Y::nat=>'a::pcpo)|]\
   260 \ ==> ? j.!i.j<i-->~Y(i)=UU"
   260 \ ==> ? j.!i.j<i-->~Y(i)=UU"
   261  (fn prems =>
   261  (fn prems =>
   262         [
   262         [
   263         (cut_facts_tac prems 1),
   263         (cut_facts_tac prems 1),
   264         (safe_tac HOL_cs),
   264         Safe_tac,
   265         (step_tac HOL_cs 1),
   265         (Step_tac 1),
   266         (strip_tac 1),
   266         (strip_tac 1),
   267         (rtac notUU_I 1),
   267         (rtac notUU_I 1),
   268         (atac 2),
   268         (atac 2),
   269         (etac (chain_mono RS mp) 1),
   269         (etac (chain_mono RS mp) 1),
   270         (atac 1)
   270         (atac 1)
   290  	(etac exE 1),
   290  	(etac exE 1),
   291         (res_inst_tac [("x","i")] exI 1),
   291         (res_inst_tac [("x","i")] exI 1),
   292         (strip_tac 1),
   292         (strip_tac 1),
   293         (dres_inst_tac [("x","i"),("y","j")] chain_mono 1),
   293         (dres_inst_tac [("x","i"),("y","j")] chain_mono 1),
   294         (etac (le_imp_less_or_eq RS disjE) 1),
   294         (etac (le_imp_less_or_eq RS disjE) 1),
   295 	(safe_tac HOL_cs),
   295 	Safe_tac,
   296 	(dtac (ax_flat RS spec RS spec RS mp) 1),
   296 	(dtac (ax_flat RS spec RS spec RS mp) 1),
   297 	(fast_tac HOL_cs 1)
   297 	(Fast_tac 1)
   298         ]);
   298         ]);
   299 
   299 
   300 (* flat subclass of chfin --> adm_flat not needed *)
   300 (* flat subclass of chfin --> adm_flat not needed *)
   301 
   301 
   302 qed_goal "flat_eq" thy "(a::'a::flat) ~= UU ==> a << b = (a = b)" 
   302 qed_goal "flat_eq" thy "(a::'a::flat) ~= UU ==> a << b = (a = b)"