Thm* p:Fmla, rho:Decl, ds,daa:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), s:{[[ds]] rho}, e:{[[de]] rho}, a1,a2:Top, tr:trace_env([[daa]] rho). trace_consistent_pred(rho;daa;tr.proj;p)  tc_pred(p;ds;da1;de)  closed_pred(p)  ([[p]] rho ds da1 de e s a1 tr  [[p]] rho ds da2 de e s a2 tr) | [closed_pred_mng] |
Thm* r:rel(), rho:Decl, ds,daa:Collection(dec()), da1,da2:Collection(SimpleType), de:sig(), s:{[[ds]] rho}, e:{[[de]] rho}, a1,a2:Top, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r)  tc(r;ds;da1;de)  closed_rel(r)  ([[r]] rho ds da1 de e s a1 tr  [[r]] rho ds da2 de e s a2 tr) | [closed_rel_mng_2] |