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Proofgold Proof
pf
Apply df_ordt__df_xrs__df_qtop__df_imas__df_qus__df_xps__df_mre__df_mrc__df_mri__df_acs__df_cat__df_cid__df_homf__df_comf__df_oppc__df_mon__df_epi__df_sect with
wceq
coppc
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
co
(
co
(
cv
x0
)
(
cop
(
cfv
cnx
chom
)
(
ctpos
(
cfv
(
cv
x0
)
chom
)
)
)
csts
)
(
cop
(
cfv
cnx
cco
)
(
cmpt2
(
λ x1 x2 .
cxp
(
cfv
(
cv
x0
)
cbs
)
(
cfv
(
cv
x0
)
cbs
)
)
(
λ x1 x2 .
cfv
(
cv
x0
)
cbs
)
(
λ x1 x2 .
ctpos
(
co
(
cop
(
cv
x2
)
(
cfv
(
cv
x1
)
c2nd
)
)
(
cfv
(
cv
x1
)
c1st
)
(
cfv
(
cv
x0
)
cco
)
)
)
)
)
csts
)
)
.
Assume H0:
wceq
cordt
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cfv
(
cfv
(
cun
(
csn
(
cdm
(
cv
x0
)
)
)
(
crn
(
cun
(
cmpt
(
λ x1 .
cdm
(
cv
x0
)
)
(
λ x1 .
crab
(
λ x2 .
wn
(
wbr
(
cv
x2
)
(
cv
x1
)
(
cv
x0
)
)
)
(
λ x2 .
cdm
(
cv
x0
)
)
)
)
(
cmpt
(
λ x1 .
cdm
(
cv
x0
)
)
(
λ x1 .
crab
(
λ x2 .
wn
(
wbr
(
cv
x1
)
(
cv
x2
)
(
cv
x0
)
)
)
(
λ x2 .
cdm
(
cv
x0
)
)
)
)
)
)
)
cfi
)
ctg
)
)
.
Assume H1:
wceq
cxrs
(
cun
(
ctp
(
cop
(
cfv
cnx
cbs
)
cxr
)
(
cop
(
cfv
cnx
cplusg
)
cxad
)
(
cop
(
cfv
cnx
cmulr
)
cxmu
)
)
(
ctp
(
cop
(
cfv
cnx
cts
)
(
cfv
cle
cordt
)
)
(
cop
(
cfv
cnx
cple
)
cle
)
(
cop
(
cfv
cnx
cds
)
(
cmpt2
(
λ x0 x1 .
cxr
)
(
λ x0 x1 .
cxr
)
(
λ x0 x1 .
cif
(
wbr
(
cv
x0
)
(
cv
x1
)
cle
)
(
co
(
cv
x1
)
(
cxne
(
cv
x0
)
)
cxad
)
(
co
(
cv
x0
)
(
cxne
(
cv
x1
)
)
cxad
)
)
)
)
)
)
.
Assume H2:
wceq
cqtop
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
crab
(
λ x2 .
wcel
(
cin
(
cima
(
ccnv
(
cv
x1
)
)
(
cv
x2
)
)
(
cuni
(
cv
x0
)
)
)
(
cv
x0
)
)
(
λ x2 .
cpw
(
cima
(
cv
x1
)
(
cuni
(
cv
x0
)
)
)
)
)
)
.
Assume H3:
wceq
cimas
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
csb
(
cfv
(
cv
x1
)
cbs
)
(
λ x2 .
cun
(
cun
(
ctp
(
cop
(
cfv
cnx
cbs
)
(
crn
(
cv
x0
)
)
)
(
cop
(
cfv
cnx
cplusg
)
(
ciun
(
λ x3 .
cv
x2
)
(
λ x3 .
ciun
(
λ x4 .
cv
x2
)
(
λ x4 .
csn
(
cop
...
...
)
)
)
)
)
...
)
...
)
...
)
)
)
.
...
■