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Proofgold Proof
pf
Apply df_ppi__df_mu__df_sgm__df_dchr__df_lgs__df_itv__df_lng__df_trkgc__df_trkgb__df_trkgcb__df_trkge__df_trkgld__df_trkg__df_cgrg__df_ismt__df_leg__df_hlg__df_mir with
wceq
cstrkgld
(
copab
(
λ x0 x1 .
wsbc
(
λ x2 .
wsbc
(
λ x3 .
wsbc
(
λ x4 .
wex
(
λ x5 .
wa
(
wf1
(
co
c1
(
cv
x1
)
cfzo
)
(
cv
x2
)
(
cv
x5
)
)
(
wrex
(
λ x6 .
wrex
(
λ x7 .
wrex
(
λ x8 .
wa
(
wral
(
λ x9 .
w3a
(
wceq
(
co
(
cfv
c1
(
cv
x5
)
)
(
cv
x6
)
(
cv
x3
)
)
(
co
(
cfv
(
cv
x9
)
(
cv
x5
)
)
(
cv
x6
)
(
cv
x3
)
)
)
(
wceq
(
co
(
cfv
c1
(
cv
x5
)
)
(
cv
x7
)
(
cv
x3
)
)
(
co
(
cfv
(
cv
x9
)
(
cv
x5
)
)
(
cv
x7
)
(
cv
x3
)
)
)
(
wceq
(
co
(
cfv
c1
(
cv
x5
)
)
(
cv
x8
)
(
cv
x3
)
)
(
co
(
cfv
(
cv
x9
)
(
cv
x5
)
)
(
cv
x8
)
(
cv
x3
)
)
)
)
(
λ x9 .
co
c2
(
cv
x1
)
cfzo
)
)
(
wn
(
w3o
(
wcel
(
cv
x8
)
(
co
(
cv
x6
)
(
cv
x7
)
(
cv
x4
)
)
)
(
wcel
(
cv
x6
)
(
co
(
cv
x8
)
(
cv
x7
)
(
cv
x4
)
)
)
(
wcel
(
cv
x7
)
(
co
(
cv
x6
)
(
cv
x8
)
(
cv
x4
)
)
)
)
)
)
(
λ x8 .
cv
x2
)
)
(
λ x7 .
cv
x2
)
)
(
λ x6 .
cv
x2
)
)
)
)
(
cfv
(
cv
x0
)
citv
)
)
(
cfv
(
cv
x0
)
cds
)
)
(
cfv
(
cv
x0
)
cbs
)
)
)
.
Assume H0:
wceq
cppi
(
cmpt
(
λ x0 .
cr
)
(
λ x0 .
cfv
(
cin
(
co
cc0
(
cv
x0
)
cicc
)
cprime
)
chash
)
)
.
Assume H1:
wceq
cmu
(
cmpt
(
λ x0 .
cn
)
(
λ x0 .
cif
(
wrex
(
λ x1 .
wbr
(
co
(
cv
x1
)
c2
cexp
)
(
cv
x0
)
cdvds
)
(
λ x1 .
cprime
)
)
cc0
(
co
(
cneg
c1
)
(
cfv
(
crab
(
λ x1 .
wbr
(
cv
x1
)
(
cv
x0
)
cdvds
)
(
λ x1 .
cprime
)
)
chash
)
cexp
)
)
)
.
Assume H2:
wceq
csgm
(
cmpt2
(
λ x0 x1 .
cc
)
(
λ x0 x1 .
cn
)
(
λ x0 x1 .
csu
(
crab
(
λ x2 .
wbr
(
cv
x2
)
(
cv
x1
)
cdvds
)
(
λ x2 .
cn
)
)
(
λ x2 .
co
(
cv
x2
)
(
cv
x0
)
ccxp
)
)
)
.
Assume H3:
wceq
cdchr
(
cmpt
(
λ x0 .
cn
)
(
λ x0 .
csb
(
cfv
(
cv
x0
)
czn
)
(
λ x1 .
csb
(
crab
(
λ x2 .
wss
(
cxp
(
cdif
(
cfv
(
cv
...
)
...
)
...
)
...
)
...
)
...
)
...
)
)
)
.
...
■