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Proofgold Proof
pf
Apply df_nrg__df_nlm__df_nvc__df_nmo__df_nghm__df_nmhm__df_ii__df_cncf__df_htpy__df_phtpy__df_phtpc__df_pco__df_om1__df_omn__df_pi1__df_pin__df_clm__df_cvs with
wceq
cii
(
cfv
(
cres
(
ccom
cabs
cmin
)
(
cxp
(
co
cc0
c1
cicc
)
(
co
cc0
c1
cicc
)
)
)
cmopn
)
.
Assume H0:
wceq
cnrg
(
crab
(
λ x0 .
wcel
(
cfv
(
cv
x0
)
cnm
)
(
cfv
(
cv
x0
)
cabv
)
)
(
λ x0 .
cngp
)
)
.
Assume H1:
wceq
cnlm
(
crab
(
λ x0 .
wsbc
(
λ x1 .
wa
(
wcel
(
cv
x1
)
cnrg
)
(
wral
(
λ x2 .
wral
(
λ x3 .
wceq
(
cfv
(
co
(
cv
x2
)
(
cv
x3
)
(
cfv
(
cv
x0
)
cvsca
)
)
(
cfv
(
cv
x0
)
cnm
)
)
(
co
(
cfv
(
cv
x2
)
(
cfv
(
cv
x1
)
cnm
)
)
(
cfv
(
cv
x3
)
(
cfv
(
cv
x0
)
cnm
)
)
cmul
)
)
(
λ x3 .
cfv
(
cv
x0
)
cbs
)
)
(
λ x2 .
cfv
(
cv
x1
)
cbs
)
)
)
(
cfv
(
cv
x0
)
csca
)
)
(
λ x0 .
cin
cngp
clmod
)
)
.
Assume H2:
wceq
cnvc
(
cin
cnlm
clvec
)
.
Assume H3:
wceq
cnmo
(
cmpt2
(
λ x0 x1 .
cngp
)
(
λ x0 x1 .
cngp
)
(
λ x0 x1 .
cmpt
(
λ x2 .
co
(
cv
x0
)
(
cv
x1
)
cghm
)
(
λ x2 .
cinf
(
crab
(
λ x3 .
wral
(
λ x4 .
wbr
(
cfv
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cv
x1
)
cnm
)
)
(
co
(
cv
x3
)
(
cfv
(
cv
x4
)
(
cfv
(
cv
x0
)
cnm
)
)
cmul
)
cle
)
(
λ x4 .
cfv
(
cv
x0
)
cbs
)
)
(
λ x3 .
co
cc0
cpnf
cico
)
)
cxr
clt
)
)
)
.
Assume H4:
wceq
cnghm
(
cmpt2
(
λ x0 x1 .
cngp
)
(
λ x0 x1 .
cngp
)
(
λ x0 x1 .
cima
(
ccnv
(
co
(
cv
x0
)
(
cv
x1
)
cnmo
)
)
cr
)
)
.
Assume H5:
wceq
cnmhm
(
cmpt2
(
λ x0 x1 .
cnlm
)
(
λ x0 x1 .
cnlm
)
(
λ x0 x1 .
cin
(
co
(
cv
x0
)
(
cv
x1
)
clmhm
)
(
co
(
cv
x0
)
(
cv
x1
)
cnghm
)
)
)
.
Assume H6:
wceq
cii
(
cfv
(
cres
(
ccom
cabs
cmin
)
(
cxp
(
co
cc0
c1
cicc
)
(
co
cc0
c1
cicc
)
)
)
cmopn
)
.
Assume H7:
wceq
ccncf
(
cmpt2
(
λ x0 x1 .
cpw
cc
)
(
λ x0 x1 .
cpw
cc
)
(
λ x0 x1 .
crab
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wrex
(
λ x5 .
wral
(
λ x6 .
...
⟶
wbr
(
cfv
(
co
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
cfv
(
cv
x6
)
(
cv
x2
)
)
cmin
)
cabs
)
(
cv
...
)
...
)
...
)
...
)
...
)
...
)
...
)
)
.
...
■