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] |
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* 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] |
Def ioa_mentions_trace(A)
== ( e:eff(). e A.eff & mentions_trace(e.smt.term))
( p:pre(). p A.pre & rel_mentions_trace(p.rel))
( r:rel(). r A.init & rel_mentions_trace(r)) | [ioa_mentions_trace] |
Def guarded_trace(da;e;I)
== r:rel(). r I  ( k:Label. affects_trace_rel(e;k;r)  ( t:dec(). t da & t.lbl = k)) | [guarded_trace] |