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Proofgold Proof
pf
Apply df_cph__df_tch__df_cfil__df_cau__df_cmet__df_cms__df_bn__df_hl__df_rrx__df_ehl__df_ovol__df_vol__df_mbf__df_itg1__df_itg2__df_ibl__df_itg__df_0p with
wceq
ccph
(
crab
(
λ x0 .
wsbc
(
λ x1 .
wsbc
(
λ x2 .
w3a
(
wceq
(
cv
x1
)
(
co
ccnfld
(
cv
x2
)
cress
)
)
(
wss
(
cima
csqrt
(
cin
(
cv
x2
)
(
co
cc0
cpnf
cico
)
)
)
(
cv
x2
)
)
(
wceq
(
cfv
(
cv
x0
)
cnm
)
(
cmpt
(
λ x3 .
cfv
(
cv
x0
)
cbs
)
(
λ x3 .
cfv
(
co
(
cv
x3
)
(
cv
x3
)
(
cfv
(
cv
x0
)
cip
)
)
csqrt
)
)
)
)
(
cfv
(
cv
x1
)
cbs
)
)
(
cfv
(
cv
x0
)
csca
)
)
(
λ x0 .
cin
cphl
cnlm
)
)
.
Assume H0:
wceq
ccph
(
crab
(
λ x0 .
wsbc
(
λ x1 .
wsbc
(
λ x2 .
w3a
(
wceq
(
cv
x1
)
(
co
ccnfld
(
cv
x2
)
cress
)
)
(
wss
(
cima
csqrt
(
cin
(
cv
x2
)
(
co
cc0
cpnf
cico
)
)
)
(
cv
x2
)
)
(
wceq
(
cfv
(
cv
x0
)
cnm
)
(
cmpt
(
λ x3 .
cfv
(
cv
x0
)
cbs
)
(
λ x3 .
cfv
(
co
(
cv
x3
)
(
cv
x3
)
(
cfv
(
cv
x0
)
cip
)
)
csqrt
)
)
)
)
(
cfv
(
cv
x1
)
cbs
)
)
(
cfv
(
cv
x0
)
csca
)
)
(
λ x0 .
cin
cphl
cnlm
)
)
.
Assume H1:
wceq
ctch
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
co
(
cv
x0
)
(
cmpt
(
λ x1 .
cfv
(
cv
x0
)
cbs
)
(
λ x1 .
cfv
(
co
(
cv
x1
)
(
cv
x1
)
(
cfv
(
cv
x0
)
cip
)
)
csqrt
)
)
ctng
)
)
.
Assume H2:
wceq
ccfil
(
cmpt
(
λ x0 .
cuni
(
crn
cxmt
)
)
(
λ x0 .
crab
(
λ x1 .
wral
(
λ x2 .
wrex
(
λ x3 .
wss
(
cima
(
cv
x0
)
(
cxp
(
cv
x3
)
(
cv
x3
)
)
)
(
co
cc0
(
cv
x2
)
cico
)
)
(
λ x3 .
cv
x1
)
)
(
λ x2 .
crp
)
)
(
λ x1 .
cfv
(
cdm
(
cdm
(
cv
x0
)
)
)
cfil
)
)
)
.
Assume H3:
wceq
cca
(
cmpt
(
λ x0 .
cuni
(
crn
cxmt
)
)
(
λ x0 .
crab
(
λ x1 .
wral
(
λ x2 .
wrex
(
λ x3 .
wf
(
cfv
(
cv
x3
)
cuz
)
(
co
(
cfv
(
cv
x3
)
(
cv
x1
)
)
(
cv
x2
)
(
cfv
(
cv
x0
)
cbl
)
)
(
cres
(
cv
x1
)
(
cfv
(
cv
x3
)
cuz
)
)
)
(
λ x3 .
cz
)
)
(
λ x2 .
crp
)
)
(
λ x1 .
co
(
cdm
(
cdm
(
cv
x0
)
)
)
cc
cpm
)
)
)
.
Assume H4:
wceq
cms
...
.
...
■