At:
wp2 correctness
4
1
1
1
1
2
1.
A: ioa{i:l}()
2.
de: sig()
3.
tc_ioa(A;de)
4.
ioa_mentions_trace(A)
5.
Q: Fmla
6.
rho: Decl
7.
e: {[[de]] rho}
8.
a: [[A]] rho de e.action
9.
tr: trace_env([[A.da]] rho)
10.
trace_consistent_pred(rho;A.da;tr.proj;Q)
11.
single_valued_decls(A.ds)
12.
s: [[A]] rho de e.state
13.
x': [[A]] rho de e.state
14.
tc_pred(Q;A.ds; < > ;de)
15.
closed_pred(Q)
16.
covers_pred(A;Q)
17.
[[A]] rho de e.trans(s,a,x')
18.
r: rel()
19.
r 
Q
20.
tc(r;A.ds; < > ;de)
21.
closed_rel(r)
22.
r@0: rel()
23.
as: (Label
Term) List
24.
1of(unzip(as)) = rel_primed_vars(r)
25.
i:
. i < ||as|| 
2of(as[i]) (
x.smts_eff(action_effect(kind(a);A.eff;A.frame);x))(1of(as[i]))
26.
r@0 = rel_subst2(as;r)
subst_mentions_trace(as)
By:
Reduce -2
THEN
BackThruLemma'
Thm* A:ioa{i:l}(), as:(LabelTerm) List, k:Label. ioa_mentions_trace(A) (i:. i < ||as|| 2of(as[i]) smts_eff(action_effect(k;A.eff;A.frame);1of(as[i]))) subst_mentions_trace(as)
Generated subgoals:
None
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