Thm* Q:Fmla. closed_pred((Q)')  closed_pred(Q) | [closed_pred_addprime] |
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(), 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] |
Thm* c:(Label Collection(Term)), r,r':rel().
r' col_subst2(c;r)

( as:(Label Term) List.
1of(unzip(as)) = rel_primed_vars(r)
& ( i: . i < ||as||  2of(as[i]) c(1of(as[i])))
& r' = rel_subst2(as;r)) | [member_col_subst2] |
Thm* Q:Fmla, A:ioa{i:l}(). covers_pred(A;(Q)')  covers_pred(A;Q) | [covers_pred_addprime] |
Thm* c:(Label Collection(Term)), r,r':rel().
r' col_subst(c;r)

( as:(Label Term) List.
1of(unzip(as)) = rel_vars(r)
& ( i: . i < ||as||  2of(as[i]) c(1of(as[i])))
& r' = rel_subst(as;r)) | [member_col_subst] |
Thm* r:rel().
rel_mentions_trace(r)  ( i: . i < ||r.args|| & mentions_trace(r.args[i])) | [rel_mentions_trace_iff] |
Thm* x:Label, r:rel().
(x rel_primed_vars(r))  ( i: . i < ||r.args|| & (x term_primed_vars(r.args[i]))) | [member_rel_primed_vars] |
Thm* as:(Label Term) List.
subst_mentions_trace(as)  ( i: ||as||. mentions_trace(2of(as[i]))) | [assert_subst_mentions_trace] |
Thm* a,b:rel(). rel_eq(a;b)  a = b | [assert_rel_eq] |