At:
accumulate wf11121
1.
A: Type
2.
B: Type
3.
P: BA
4.
F: BAA
5.
G: BAA
6.
H: BAA
7.
N: BA(B List)
8.
M: A
9.
i:B, s:A. P(i,s) M(F(i,s))M(s)
10.
i:B, s:A. M(G(i,s))M(s)
11.
i:B, s:A. P(i,s) M(H(i,s)) < M(s)
12.
m:
13.
m1:.
m1 < m
(u:A.
M(u) = m1
(j:B.
process u j where
process s i ==
if P(i,s) then F(i,s)
else G(i,s) where
xs := N(i,s);
s:= H(i,s);
while not null xs {
s := process s (hd xs);
xs := tl xs;
}
{s:A| M(s)M(u) }))
14.
u: A
15.
M(u) = m
16.
j: B
17.
P(j,u)
18.
z: B List
19.
u1: B
20.
v: B List
21.
a:{s:A| M(s)M(H(j,u)) }.
list_accum(s',i'.process s' i' where
process s i ==
if P(i,s) then F(i,s)
else G(i,s) where
xs := N(i,s);
s:= H(i,s);
while not null xs {
s := process s (hd xs);
xs := tl xs;
} ;a;v)
{s:A| M(s)M(a) }
22.
a: {s:A| M(s)M(H(j,u)) }
23.
s': {s:A| M(s)M(a) }
24.
i': B
M(s') < m
By:
Analyze -3
THEN
Analyze -2
THEN
AssertBY (M(H(j,u)) < M(u)) EasyHyp
Generated subgoals: