At:
closed pred mng1111
1.
p: Fmla
2.
rho: Decl
3.
ds: Collection(dec())
4.
daa: Collection(dec())
5.
da1: Collection(SimpleType)
6.
da2: Collection(SimpleType)
7.
de: sig()
8.
s: {[[ds]] rho}
9.
e: {[[de]] rho}
10.
a1: Top
11.
a2: Top
12.
tr: trace_env([[daa]] rho)
13.
trace_consistent_pred(rho;daa;tr.proj;p)
14.
tc_pred(p;ds;da1;de)
15.
closed_pred(p)
16.
r: rel()
17.
r p
[[r]] rho ds da1 de e s a1 tr ~ [[r]] rho ds da1 de e s tr
By:
BackThru
Thm*r:rel(), rho,ds,da1,da2,de,s,e,a1,a2,tr:Top. closed_rel(r) ([[r]] rho ds da1 de e s a1 tr ~ [[r]] rho ds da2 de e s a2 tr)
THEN
EasyHypThen Auto
Generated subgoals:
p
[[r]] rho ds da1 de e s a1 tr ~ [[r]] rho ds da1 de e s 
tr
r:rel(), rho,ds,da1,da2,de,s,e,a1,a2,tr:Top. closed_rel(r) 
([[r]] rho ds da1 de e s a1 tr ~ [[r]] rho ds da2 de e s a2 tr)