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Proofgold Proof
pf
Apply df_mfsh__df_mevl__df_mvl__df_mvsb__df_mfrel__df_mdl__df_musyn__df_gmdl__df_mitp__df_mfitp__df_irng__df_cplmet__df_homlimb__df_homlim__df_plfl__df_sfl1__df_sfl__df_psl with
wceq
cpfl
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
csb
(
cfv
(
cv
x0
)
cpl1
)
(
λ x2 .
csb
(
cfv
(
csn
(
cv
x1
)
)
(
cfv
(
cv
x2
)
crsp
)
)
(
λ x3 .
csb
(
cmpt
(
λ x4 .
cfv
(
cv
x0
)
cbs
)
(
λ x4 .
cec
(
co
(
cv
x4
)
(
cfv
(
cv
x2
)
cur
)
(
cfv
(
cv
x2
)
cvsca
)
)
(
co
(
cv
x2
)
(
cv
x3
)
cqg
)
)
)
(
λ x4 .
cop
(
csb
(
co
(
cv
x2
)
(
co
(
cv
x2
)
(
cv
x3
)
cqg
)
cqus
)
(
λ x5 .
co
(
co
(
cv
x5
)
(
crio
(
λ x6 .
wceq
(
ccom
(
cv
x6
)
(
cv
x4
)
)
(
cfv
(
cv
x0
)
cnm
)
)
(
λ x6 .
cfv
(
cv
x5
)
cabv
)
)
ctng
)
(
cop
(
cfv
cnx
cple
)
(
csb
(
cmpt
(
λ x6 .
cfv
(
cv
x5
)
cbs
)
(
λ x6 .
crio
(
λ x7 .
wbr
(
co
(
cv
x0
)
(
cv
x7
)
cdg1
)
(
co
(
cv
x0
)
(
cv
x1
)
cdg1
)
clt
)
(
λ x7 .
cv
x6
)
)
)
(
λ x6 .
ccom
(
ccnv
(
cv
x6
)
)
(
ccom
(
cfv
(
cv
x2
)
cple
)
(
cv
x6
)
)
)
)
)
csts
)
)
(
cv
x4
)
)
)
)
)
)
.
Assume H0:
wceq
cmfsh
(
cslot
c8
)
.
Assume H1:
wceq
cmevl
(
cslot
c9
)
.
Assume H2:
wceq
cmvl
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cixp
(
λ x1 .
cfv
(
cv
x0
)
cmvar
)
(
λ x1 .
cima
(
cfv
(
cv
x0
)
cmuv
)
(
csn
(
cfv
(
cv
x1
)
(
cfv
(
cv
x0
)
cmty
)
)
)
)
)
)
.
Assume H3:
wceq
cmvsb
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
coprab
(
λ x1 x2 x3 .
w3a
(
wa
(
wcel
(
cv
x1
)
(
crn
(
cfv
(
cv
x0
)
cmsub
)
)
)
(
wcel
(
cv
x2
)
(
cfv
(
cv
x0
)
cmvl
)
)
)
(
wral
(
λ x4 .
wbr
(
cv
x2
)
(
cfv
(
cfv
(
cv
x4
)
(
cfv
(
cv
x0
)
cmvh
)
)
(
cv
x1
)
)
(
cdm
(
cfv
(
cv
x0
)
cmevl
)
)
)
(
λ x4 .
cfv
(
cv
x0
)
cmvar
)
)
(
wceq
(
cv
x3
)
(
cmpt
(
λ x4 .
cfv
(
cv
x0
)
cmvar
)
(
λ x4 .
co
(
cv
x2
)
(
cfv
(
cfv
(
cv
x4
)
(
cfv
(
cv
x0
)
cmvh
)
)
(
cv
x1
)
)
(
cfv
(
cv
x0
)
cmevl
)
)
)
)
)
)
)
.
Assume H4:
wceq
cmfr
(
cmpt
(
λ x0 .
cvv
)
...
)
.
...
■