| Rank | Theorem | Name |
| 7 | | | Thm*  A:ioa{i:l}(), r:rel(), rho:Decl, de:sig(), e:{[[de]] rho}, a:( [[A.da]] rho), tr:trace_env([[A.da]] rho). tc_ioa(A;de)    ioa_mentions_trace(A) trace_consistent_rel(rho;A.da;tr.proj;r) single_valued_decls(A.ds) (s,x':[[A]] rho de e.state. tc(r;A.ds;dec_lookup(A.da;kind(a));de) covers_rel(A;r) [[A]] rho de e.trans(s,a,x') (rel_mng_2(r; rho; A.ds; dec_lookup(A.da;kind(a)); de; e; s; x'; value(a); tr)  [[wp2_rel(A;kind(a);r)]] rho A.ds dec_lookup(A.da;kind(a)) de e s value(a) tr)) | [wp2_rel_correct] |
| cites |
| 0 | | | Thm* v:Top, rho:Decl. v  [[ < > ]] rho | [empty_sts_mng] |
| 1 | | | Thm* ds:Collection(dec()), rho:Decl, a:([[ds]] rho). value(a) [[dec_lookup(ds;kind(a))]] rho | [sigma_decls_mng_value] |
| 2 | | | 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] |
| 6 | | | 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] |
| 1 | | | Thm* as:(LabelT) List, d:T, x:Label. (x 1of(unzip(as))) ( < x,apply_alist(as;x;d) > as) | [apply_alist_member] |
| 2 | | | Thm* ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), t:Term. ds1  ds2 da1 da2 (a:SimpleType. a term_types(ds1;da1;de;t) a term_types(ds2;da2;de;t)) | [term_types_monotone_member] |
| 0 | | | Thm* ds:Collection(dec()), x:Label, T:SimpleType. T dec_lookup(ds;x) mk_dec(x, T) ds | [member_dec_lookup] |
| 3 | | | Thm* r:rel(), as:(LabelTerm) 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] |
| 4 | | | Thm* A:ioa{i:l}(), Q:Fmla, de:sig(), a:Label. tc_ioa(A;de) tc_pred(Q;A.ds;dec_lookup(A.da;a);de) single_valued_decls(A.ds) tc_pred(wp2(A;a;Q);A.ds;dec_lookup(A.da;a);de) | [tc_wp2] |