| Rank | Theorem | Name |
| 5 | | | Thm*  r1,r2:rel(), ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, e:{[[de]] rho}, s1,s2:{[[ds]] rho}, a:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent_rel(rho;daa;tr.proj;r1)   trace_consistent_rel(rho;daa;tr.proj;r2) tc(r1;ds;da;de) tc(r2;ds;da;de) r1.name = r2.name ||r1.args|| = ||r2.args||   (i:. i < ||r1.args|| [[r1.args[i]]] 1of(e) s1 a tr = [[r2.args[i]]] 1of(e) s1 s2 a tr [[rel_arg_typ(r1.name;i;de)]] rho) ([[r1]] rho ds da de e s1 a tr  rel_mng_2(r2; rho; ds; da; de; e; s1; s2; a; tr)) | [rel_mng_2_iff] |
| cites |
| 3 | | | Thm* r:rel(), i:, ds,da:Collection(dec()), st1:Collection(SimpleType), de:sig(), rho:Decl, s,s':{[[ds]] rho}, e:{1of([[de]] rho)}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) i < ||r.args|| [[r.args[i]]] e s s' a tr [[rel_arg_typ(r.name;i;de)]] rho | [rel_arg_typing2] |
| 4 | | | Thm* r:rel(), i:, ds,da:Collection(dec()), st1:Collection(SimpleType), de:sig(), rho:Decl, s:{[[ds]] rho}, e:{1of([[de]] rho)}, a:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent_rel(rho;da;tr.proj;r) tc(r;ds;st1;de) i < ||r.args|| [[r.args[i]]] e s a tr [[rel_arg_typ(r.name;i;de)]] rho | [rel_arg_typing] |
| 0 | | | Thm* z:T List. ||z|| = 2 z = [z[0]; z[1]] | [list_2_decomp] |
| 4 | | | Thm* ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType), e1:{1of([[de]] rho)}, s:{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho), l:Term List. (i:||l||. trace_consistent(rho;da;tr.proj;l[i])) (ls:SimpleType List, f:reduce( s,m. [[s]] rho  m;Prop;ls). ||ls|| = ||l|| & (i:. i < ||l|| ls[i] term_types(ds;st1;de;l[i])) list_accum(x,t.x([[t]] e1 s a tr);f;l) Prop) | [rel_mng_lemma] |
| 3 | | | Thm* ds,da:Collection(dec()), de:sig(), rho:Decl, st1:Collection(SimpleType), e1:{1of([[de]] rho)}, s,s':{[[ds]] rho}, a:[[st1]] rho, tr:trace_env([[da]] rho), l:Term List. (i:||l||. trace_consistent(rho;da;tr.proj;l[i])) (ls:SimpleType List, f:reduce(s,m. [[s]] rhom;Prop;ls). ||ls|| = ||l|| & (i:. i < ||l|| ls[i] term_types(ds;st1;de;l[i])) list_accum(x,t.x([[t]] e1 s s' a tr);f;l) Prop) | [rel_mng_2_lemma] |
| 0 | | | Thm* x:T, l:T List, i:||l||. [x / l][(i+1)] ~ l[i] | [select_cons_tl_sq] |
| 3 | | | Thm* ds,da:Collection(dec()), st1:Collection(SimpleType), de:sig(), rho:Decl, t:Term, s:{[[ds]] rho}, e:{1of([[de]] rho)}, a:SimpleType, v:[[st1]] rho, tr:trace_env([[da]] rho). trace_consistent(rho;da;tr.proj;t) a term_types(ds;st1;de;t) [[t]] e s v tr [[a]] rho | [term_typing] |
| 2 | | | Thm* ds,daa:Collection(dec()), da:Collection(SimpleType), de:sig(), rho:Decl, t:Term, s,s':{[[ds]] rho}, e:{1of([[de]] rho)}, a:SimpleType, v:[[da]] rho, tr:trace_env([[daa]] rho). trace_consistent(rho;daa;tr.proj;t) a term_types(ds;da;de;t) [[t]] e s s' v tr [[a]] rho | [term_typing2] |