is mentioned by
Thm* rho:Decl, r:rel(), da:Collection(dec()) , R:(LabelLabel). rel_mentions_trace(r) trace_consistent_rel(rho;da;R;r) | [no_mention_implies_consistent_rel] |
Thm* A:ioa{i:l}(), a:Label, Q:Fmla. wp2(A;a;Q) Fmla | [wp2_wf] |
Thm* A:ioa{i:l}(), as:(LabelTerm) List, k:Label. ioa_mentions_trace(A) (i:. i < ||as|| 2of(as[i]) smts_eff(action_effect(k;A.eff;A.frame);1of(as[i]))) subst_mentions_trace(as) | [effect_subst_mentions_trace] |
Thm* ds,da:Collection(dec()), st:Collection(SimpleType), de:sig(), rho:Decl , e1:{1of([[de]] rho)}, s1,s2:{[[ds]] rho}, a:[[st]] rho, tr:trace_env([[da]] rho), u:Term , t:SimpleType. trace_consistent(rho;da;tr.proj;u) (x:Label. (x term_vars(u)) s1.x = s2.x) t term_types(ds;st;de;u) [[u]] e1 s1 a tr = [[u]] e1 s2 a tr [[t]] rho | [term_mng_equal] |
Thm* r:rel(), as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) (x:Label. (x rel_vars(r)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) tc(rel_subst(as;r);ds;da;de) | [rel_subst_tc] |
Thm* r:rel(), as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). tc(r;ds;da;de) (x:Label. (x rel_primed_vars(r)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) tc(rel_subst2(as;r);ds;da;de) | [rel_subst2_tc] |
Thm* da:Collection(dec()), rho:Decl, tr:trace_env([[da]] rho), y1:Label. trace_consistent(rho;da;tr.proj;trace(y1)) tr.y1 [[lbl_pr( < Trace, y1 > )]] rho | [tproj_w_f2] |
Thm* r:rel(), I:Fmla, A:ioa{i:l}(), a:Label. covers_pred(A;I) r I (r':rel(). r' col_subst2(x.smts_eff(action_effect(a;A.eff;A.frame);x);r)) | [covers_pred_lemma2] |
Thm* rho:Decl, t:Term, da:Collection(dec()), R:(LabelLabel). trace_consistent(rho;da;R;t) Prop | [trace_consistent_wf] |
Thm* rho:Decl, t:Term, da:Collection(dec()) , R:(LabelLabel). mentions_trace(t) trace_consistent(rho;da;R;t) | [no_mention_implies_consistent_term] |
Thm* c:(LabelCollection(Term)), r,r':rel(). r' col_subst2(c;r) (as:(LabelTerm) List. 1of(unzip(as)) = rel_primed_vars(r) & (i:. i < ||as|| 2of(as[i]) c(1of(as[i]))) & r' = rel_subst2(as;r)) | [member_col_subst2] |
Thm* c:(LabelCollection(Term)), r:rel(). col_subst(c;r) Collection(rel()) | [col_subst_wf_2] |
Thm* c:(LabelCollection(Term)), r,r':rel(). r' col_subst(c;r) (as:(LabelTerm) List. 1of(unzip(as)) = rel_vars(r) & (i:. i < ||as|| 2of(as[i]) c(1of(as[i]))) & r' = rel_subst(as;r)) | [member_col_subst] |
Thm* r:rel(), x:Label. (x rel_primed_vars(r)) (x rel_vars(r)) | [rel_primed_vars_rel_vars] |
Thm* r:rel(). rel_primed_vars((r)') = rel_vars(r) | [rel_vars_addprime] |
Thm* x:Label, r:rel(). (x rel_primed_vars(r)) (i:. i < ||r.args|| & (x term_primed_vars(r.args[i]))) | [member_rel_primed_vars] |
Thm* ds:Collection(dec()), rho:Decl, a:([[ds]] rho), x:Label. mk_dec(kind(a), x) ds value(a) rho(x) | [sigma_decls_mng_value2] |
Thm* ds:Collection(dec()), rho:Decl, s:{[[ds]] rho}, x:Label , t:SimpleType. t dec_lookup(ds;x) s.x [[t]] rho | [record_select_wf_decls_mng2] |
Thm* ds:Collection(dec()), rho:Decl, s:{[[ds]] rho}, x:Label , t:SimpleType. mk_dec(x, t) ds s.x [[t]] rho | [record_select_wf_decls_mng] |
Thm* da:Collection(dec()), rho:Decl, k:Label, w:[[dec_lookup(da;k)]] rho. < k,w > ([[da]] rho) | [sigma_decls_mng2] |
Thm* da:Collection(dec()), rho:Decl, tr:trace_env([[da]] rho), y1:Label. tr.y1 {a:([[da]] rho)| tr.proj(y1,kind(a)) } List | [tproj_w_f] |
Thm* r:rel(), te:(LabelLabel), rho,ds,da,de,e,s,a:Top. [[r]] rho ds da de e s a mk_trace_env(nil, te) ~ [[r]] rho ds da de e s a niltrace() | [rel_mng_nil] |
Thm* ds1,ds2:Collection(dec()), x,y:Label, rho:Decl , v:[[ds1]] rho(x). (d:dec(). d ds2 d.lbl = y mk_dec(x, d.typ) ds1) v [[ds2]] rho(y) | [decls_mng_rename_member] |
Thm* ds:Collection(dec()), rho:Decl, x:Label, y:[[ds]] rho(x) , a:SimpleType. mk_dec(x, a) ds y [[a]] rho | [decls_mng_subtype] |
Thm* ds1,ds2:Collection(dec()), x:Label, rho:Decl, v:[[ds1]] rho(x). (d:dec(). d ds2 d.lbl = x d ds1) v [[ds2]] rho(x) | [decls_mng_member] |
Thm* v:Top, rho:Decl, x:Label. v [[ < > ]] rho(x) | [empty_decls_mng] |
Thm* r:rel(), as:(LabelTerm) List. (x:Label. unprime(apply_alist(as;x;x)) = x) rel_unprime(rel_subst(as;r)) = rel_unprime(r) | [trivial_rel_subst] |
Thm* t:Term, s:SimpleType, as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). s term_types(ds;da;de;t) (x:Label. (x term_primed_vars(t)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) s term_types(ds;da;de;term_subst2(as;t)) | [term_subst2_tc] |
Thm* t:Term, s:SimpleType, as:(LabelTerm) List, ds:Collection(dec()) , da:Collection(SimpleType), de:sig(). s term_types(ds;da;de;t) (x:Label. (x term_vars(t)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)))) s term_types(ds;da;de;term_subst(as;t)) | [term_subst_tc] |
Thm* t:Term, as:(LabelTerm) List. (x:Label. unprime(apply_alist(as;x;x)) = x) unprime(term_subst(as;t)) = unprime(t) | [trivial_term_subst] |
Thm* t:pre(). t.kind Label | [pre_kind_wf] |
Thm* as:(LabelTerm) List, g:Label, t:Term. subst_mentions_trace(as) term_mentions_guard(g;term_subst2(as;t)) term_mentions_guard(g;t) | [term_subst2_mentions_guard] |
Thm* as:(LabelTerm) List, g:Label, t:Term. subst_mentions_trace(as) term_mentions_guard(g;term_subst(as;t)) term_mentions_guard(g;t) | [term_subst_mentions_guard] |
Thm* as:(LabelTerm) List. subst_mentions_trace(as) (i:||as||. mentions_trace(2of(as[i]))) | [assert_subst_mentions_trace] |
Def guarded_trace(da;e;I) == r:rel(). r I (k:Label. affects_trace_rel(e;k;r) (t:dec(). t da & t.lbl = k)) | [guarded_trace] |
Def trace_consistent(rho;da;R;t) == g:Label. term_mentions_guard(g;t) subtype_rel(({a:([[da]] rho)| (R(g,kind(a))) } List); (rho(lbl_pr( < Trace, g > )))) | [trace_consistent] |
Def col_subst2(c;r) == col_map_subst(as.rel_subst2(as;r); < zip(rel_primed_vars(r);s) | s col_list_prod(map(c;rel_primed_vars(r))) > ) | [col_subst2] |
Def col_subst(c;r) == col_map_subst(as.rel_subst(as;r); < zip(rel_vars(r);s) | s col_list_prod(map(c;rel_vars(r))) > ) | [col_subst] |
Def covers_pred(A;p) == x:Label. pred_mentions(p;x) covers_var(A;x) | [covers_pred] |
Def closed_rel(r) == rel_free_vars(r) = nil | [closed_rel] |
Def pre() == LabelLabelrel() | [pre] |
In prior sections: mb label mb declaration mb events mb automata 1 mb automata 2 mb state machine mb record
Try larger context: GenAutomata