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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
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
(
cop
(
cfv
(
cv
x3
)
(
cv
x0
)
)
(
cfv
(
cv
x4
)
(
cv
x0
)
)
)
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x1
)
cplusg
)
)
(
cv
x0
)
)
)
)
)
)
)
(
cop
(
cfv
cnx
cmulr
)
(
ciun
(
λ x3 .
cv
x2
)
(
λ x3 .
ciun
(
λ x4 .
cv
x2
)
(
λ x4 .
csn
(
cop
(
cop
(
cfv
(
cv
x3
)
(
cv
x0
)
)
(
cfv
(
cv
x4
)
(
cv
x0
)
)
)
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x1
)
cmulr
)
)
(
cv
x0
)
)
)
)
)
)
)
)
(
ctp
(
cop
(
cfv
cnx
csca
)
(
cfv
(
cv
x1
)
csca
)
)
(
cop
(
cfv
cnx
cvsca
)
(
ciun
(
λ x3 .
cv
x2
)
(
λ x3 .
cmpt2
(
λ x4 x5 .
cfv
(
cfv
(
cv
x1
)
csca
)
cbs
)
(
λ x4 x5 .
csn
(
cfv
(
cv
x3
)
(
cv
x0
)
)
)
(
λ x4 x5 .
cfv
(
co
(
cv
x4
)
(
cv
x3
)
(
cfv
(
cv
x1
)
cvsca
)
)
(
cv
x0
)
)
)
)
)
(
cop
(
cfv
cnx
cip
)
(
ciun
(
λ x3 .
cv
x2
)
(
λ x3 .
ciun
(
λ x4 .
cv
x2
)
(
λ x4 .
csn
(
cop
(
cop
(
cfv
(
cv
x3
)
(
cv
x0
)
)
(
cfv
(
cv
x4
)
(
cv
x0
)
)
)
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x1
)
cip
)
)
)
)
)
)
)
)
)
(
ctp
(
cop
(
cfv
cnx
cts
)
(
co
(
cfv
(
cv
x1
)
ctopn
)
(
cv
x0
)
cqtop
)
)
(
cop
(
cfv
cnx
cple
)
(
ccom
(
ccom
(
cv
x0
)
(
cfv
(
cv
x1
)
cple
)
)
(
ccnv
(
cv
x0
)
)
)
)
(
cop
(
cfv
cnx
cds
)
(
cmpt2
(
λ x3 x4 .
crn
(
cv
x0
)
)
(
λ x3 x4 .
crn
(
cv
x0
)
)
(
λ x3 x4 .
cinf
(
ciun
(
λ x5 .
cn
)
(
λ x5 .
crn
(
cmpt
(
λ x6 .
crab
(
λ x7 .
w3a
(
wceq
(
cfv
(
cfv
(
cfv
c1
(
cv
x7
)
)
c1st
)
(
cv
x0
)
)
(
cv
x3
)
)
(
wceq
(
cfv
(
cfv
(
cfv
...
...
)
...
)
...
)
...
)
...
)
...
)
...
)
)
)
...
...
)
)
)
)
)
)
)
.
...
■