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Proofgold Proof
pf
Apply df_vts__ax_hgt749__ax_ros335__ax_ros336__df_trkg2d__df_afs__df_bnj17__df_bnj14__df_bnj13__df_bnj15__df_bnj18__df_bnj19__ax_7d__ax_8d__ax_9d1__ax_9d2__ax_10d__ax_11d with
wceq
cafs
(
cmpt
(
λ x0 .
cstrkg
)
(
λ x0 .
copab
(
λ x1 x2 .
wsbc
(
λ x3 .
wsbc
(
λ x4 .
wsbc
(
λ x5 .
wrex
(
λ x6 .
wrex
(
λ x7 .
wrex
(
λ x8 .
wrex
(
λ x9 .
wrex
(
λ x10 .
wrex
(
λ x11 .
wrex
(
λ x12 .
wrex
(
λ x13 .
w3a
(
wceq
(
cv
x1
)
(
cop
(
cop
(
cv
x6
)
(
cv
x7
)
)
(
cop
(
cv
x8
)
(
cv
x9
)
)
)
)
(
wceq
(
cv
x2
)
(
cop
(
cop
(
cv
x10
)
(
cv
x11
)
)
(
cop
(
cv
x12
)
(
cv
x13
)
)
)
)
(
w3a
(
wa
(
wcel
(
cv
x7
)
(
co
(
cv
x6
)
(
cv
x8
)
(
cv
x5
)
)
)
(
wcel
(
cv
x11
)
(
co
(
cv
x10
)
(
cv
x12
)
(
cv
x5
)
)
)
)
(
wa
(
wceq
(
co
(
cv
x6
)
(
cv
x7
)
(
cv
x4
)
)
(
co
(
cv
x10
)
(
cv
x11
)
(
cv
x4
)
)
)
(
wceq
(
co
(
cv
x7
)
(
cv
x8
)
(
cv
x4
)
)
(
co
(
cv
x11
)
(
cv
x12
)
(
cv
x4
)
)
)
)
(
wa
(
wceq
(
co
(
cv
x6
)
(
cv
x9
)
(
cv
x4
)
)
(
co
(
cv
x10
)
(
cv
x13
)
(
cv
x4
)
)
)
(
wceq
(
co
(
cv
x7
)
(
cv
x9
)
(
cv
x4
)
)
(
co
(
cv
x11
)
(
cv
x13
)
(
cv
x4
)
)
)
)
)
)
(
λ x13 .
cv
x3
)
)
(
λ x12 .
cv
x3
)
)
(
λ x11 .
cv
x3
)
)
(
λ x10 .
cv
x3
)
)
(
λ x9 .
cv
x3
)
)
(
λ x8 .
cv
x3
)
)
(
λ x7 .
cv
x3
)
)
(
λ x6 .
cv
x3
)
)
(
cfv
(
cv
x0
)
citv
)
)
(
cfv
(
cv
x0
)
cds
)
)
(
cfv
(
cv
x0
)
cbs
)
)
)
)
.
Assume H0:
wceq
cvts
(
cmpt2
(
λ x0 x1 .
co
cc
cn
cmap
)
(
λ x0 x1 .
cn0
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cc
)
(
λ x2 .
csu
(
co
c1
(
cv
x1
)
cfz
)
(
λ x3 .
co
(
cfv
(
cv
x3
)
(
cv
x0
)
)
(
cfv
(
co
(
co
ci
(
co
c2
cpi
cmul
)
cmul
)
(
co
(
cv
x3
)
(
cv
x2
)
cmul
)
cmul
)
ce
)
cmul
)
)
)
)
.
Assume H1:
wral
(
λ x0 .
...
⟶
wrex
(
λ x1 .
wrex
(
λ x2 .
w3a
(
wral
(
λ x3 .
wbr
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
co
c1
(
cdp2
cc0
(
cdp2
c7
(
cdp2
c9
(
cdp2
c9
(
cdp2
...
...
)
)
)
)
)
...
)
...
)
...
)
...
...
)
...
)
...
)
...
.
...
■