Thm* as:(Label Term) List, A:ioa{i:l}(), de:sig(), x:Label, t:SimpleType, k:Label. single_valued_decls(A.ds)  tc_ioa(A;de)  ( i: . i < ||as||  2of(as[i]) smts_eff(action_effect(k;A.eff;A.frame);1of(as[i])))  mk_dec(x, t) A.ds  t term_types(A.ds;dec_lookup(A.da;k);de;apply_alist(as;x;x)) | [tc_ioa_lemma] |
Thm* r:rel(), as:(Label Term) List, ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s,s':{[[ds]] rho}, k:Label, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r)  tc(r;ds;da;de)  subst_mentions_trace(as)  ( 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)) & s'.x = [[apply_alist(as;x;x)]] 1of(e) s a tr [[t]] rho))  tc(rel_subst2(as;r);ds;da;de) & trace_consistent_rel(rho;daa;tr.proj;rel_subst2(as;r)) & ([[rel_subst2(as;r)]] rho ds da de e s a tr  rel_mng_2(r; rho; ds; da; de; e; s; s'; a; tr)) | [rel_subst_mng_2_iff] |
Thm* r:rel(), as:(Label Term) List, daa:Collection(dec()), rho:Decl, te:(Label Label  ). trace_consistent_rel(rho;daa;te;r)  subst_mentions_trace(as)  trace_consistent_rel(rho;daa;te;rel_subst2(as;r)) | [trace_consistent_rel_subst2] |
Thm* r:rel(), as:(Label Term) List, daa:Collection(dec()), rho:Decl, te:(Label Label  ). trace_consistent_rel(rho;daa;te;r)  subst_mentions_trace(as)  trace_consistent_rel(rho;daa;te;rel_subst(as;r)) | [trace_consistent_rel_subst] |