Thm* r:rel(), de:sig(), ds1,ds2:Collection(dec())
, da1,da2:Collection(SimpleType). ds1 ds2  da1 da2  tc(r;ds1;da1;de)  tc(r;ds2;da2;de) | [tc_monotone] |
Thm* r:rel(), as:(Label Term) 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:(Label Term) 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* r:rel(), ds:Collection(dec()), da:Collection(SimpleType), de:sig().
tc(r;ds;da;de)  tc(rel_unprime(r);ds;da;de) | [tc_unprime] |
Thm* r:rel(), ds:Collection(dec()), da:Collection(SimpleType), de:sig().
tc(r;ds;da;de)  tc((r)';ds;da;de) | [tc_addprime] |
Thm* r:rel(), ds:Collection(dec()), da1,da2:Collection(SimpleType), de:sig().
closed_rel(r)  tc(r;ds;da1;de)  tc(r;ds;da2;de) | [tc_closed_rel] |
Thm* r:rel(), ds1,ds2:Collection(dec()), da1,da2:Collection(SimpleType)
, de:sig(). ds1 = ds2  da1 = da2  (tc(r;ds1;da1;de)  tc(r;ds2;da2;de)) | [tc_functionality] |