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Proofgold Proof
pf
Apply df_coda__df_homa__df_arw__df_ida__df_coa__df_setc__df_catc__df_estrc__df_xpc__df_1stf__df_2ndf__df_prf__df_evlf__df_curf__df_uncf__df_diag__df_hof__df_yon with
wceq
c1stf
(
cmpt2
(
λ x0 x1 .
ccat
)
(
λ x0 x1 .
ccat
)
(
λ x0 x1 .
csb
(
cxp
(
cfv
(
cv
x0
)
cbs
)
(
cfv
(
cv
x1
)
cbs
)
)
(
λ x2 .
cop
(
cres
c1st
(
cv
x2
)
)
(
cmpt2
(
λ x3 x4 .
cv
x2
)
(
λ x3 x4 .
cv
x2
)
(
λ x3 x4 .
cres
c1st
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
co
(
cv
x0
)
(
cv
x1
)
cxpc
)
chom
)
)
)
)
)
)
)
.
Assume H0:
wceq
ccoda
(
ccom
c2nd
c1st
)
.
Assume H1:
wceq
choma
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cmpt
(
λ x1 .
cxp
(
cfv
(
cv
x0
)
cbs
)
(
cfv
(
cv
x0
)
cbs
)
)
(
λ x1 .
cxp
(
csn
(
cv
x1
)
)
(
cfv
(
cv
x1
)
(
cfv
(
cv
x0
)
chom
)
)
)
)
)
.
Assume H2:
wceq
carw
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cuni
(
crn
(
cfv
(
cv
x0
)
choma
)
)
)
)
.
Assume H3:
wceq
cida
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cmpt
(
λ x1 .
cfv
(
cv
x0
)
cbs
)
(
λ x1 .
cotp
(
cv
x1
)
(
cv
x1
)
(
cfv
(
cv
x1
)
(
cfv
(
cv
x0
)
ccid
)
)
)
)
)
.
Assume H4:
wceq
ccoa
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cmpt2
(
λ x1 x2 .
cfv
(
cv
x0
)
carw
)
(
λ x1 x2 .
crab
(
λ x3 .
wceq
(
cfv
(
cv
x3
)
ccoda
)
(
cfv
(
cv
x1
)
cdoma
)
)
(
λ x3 .
cfv
(
cv
x0
)
carw
)
)
(
λ x1 x2 .
cotp
(
cfv
(
cv
x2
)
cdoma
)
(
cfv
(
cv
x1
)
ccoda
)
(
co
(
cfv
(
cv
x1
)
c2nd
)
(
cfv
(
cv
x2
)
c2nd
)
(
co
(
cop
(
cfv
(
cv
x2
)
cdoma
)
(
cfv
(
cv
x1
)
cdoma
)
)
(
cfv
(
cv
x1
)
ccoda
)
(
cfv
(
cv
x0
)
cco
)
)
)
)
)
)
.
Assume H5:
wceq
csetc
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
ctp
(
cop
(
cfv
cnx
cbs
)
(
cv
x0
)
)
(
cop
(
cfv
cnx
chom
)
(
cmpt2
(
λ x1 x2 .
cv
x0
)
(
λ x1 x2 .
cv
x0
)
(
λ x1 x2 .
co
(
cv
x2
)
(
cv
x1
)
cmap
)
)
)
(
cop
(
cfv
cnx
cco
)
(
cmpt2
(
λ x1 x2 .
cxp
(
cv
x0
)
(
cv
x0
)
)
(
λ x1 x2 .
cv
x0
)
(
λ x1 x2 .
cmpt2
(
λ x3 x4 .
co
(
cv
x2
)
(
cfv
(
cv
x1
)
c2nd
)
cmap
)
(
λ x3 x4 .
co
(
cfv
(
cv
x1
)
c2nd
)
(
cfv
(
cv
x1
)
...
)
...
)
...
)
)
)
)
)
.
...
■