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Proofgold Proof
pf
Apply df_tayl__df_ana__df_ulm__df_log__df_cxp__df_logb__df_asin__df_acos__df_atan__df_area__df_em__df_zeta__df_lgam__df_gam__df_igam__df_cht__df_vma__df_chp with
wceq
cana
(
cmpt
(
λ x0 .
cpr
cr
cc
)
(
λ x0 .
crab
(
λ x1 .
wral
(
λ x2 .
wcel
(
cv
x2
)
(
cfv
(
cdm
(
cin
(
cv
x1
)
(
co
cpnf
(
cv
x2
)
(
co
(
cv
x0
)
(
cv
x1
)
ctayl
)
)
)
)
(
cfv
(
co
(
cfv
ccnfld
ctopn
)
(
cv
x0
)
crest
)
cnt
)
)
)
(
λ x2 .
cdm
(
cv
x1
)
)
)
(
λ x1 .
co
cc
(
cv
x0
)
cpm
)
)
)
.
Assume H0:
wceq
ctayl
(
cmpt2
(
λ x0 x1 .
cpr
cr
cc
)
(
λ x0 x1 .
co
cc
(
cv
x0
)
cpm
)
(
λ x0 x1 .
cmpt2
(
λ x2 x3 .
cun
cn0
(
csn
cpnf
)
)
(
λ x2 x3 .
ciin
(
λ x4 .
cin
(
co
cc0
(
cv
x2
)
cicc
)
cz
)
(
λ x4 .
cdm
(
cfv
(
cv
x4
)
(
co
(
cv
x0
)
(
cv
x1
)
cdvn
)
)
)
)
(
λ x2 x3 .
ciun
(
λ x4 .
cc
)
(
λ x4 .
cxp
(
csn
(
cv
x4
)
)
(
co
ccnfld
(
cmpt
(
λ x5 .
cin
(
co
cc0
(
cv
x2
)
cicc
)
cz
)
(
λ x5 .
co
(
co
(
cfv
(
cv
x3
)
(
cfv
(
cv
x5
)
(
co
(
cv
x0
)
(
cv
x1
)
cdvn
)
)
)
(
cfv
(
cv
x5
)
cfa
)
cdiv
)
(
co
(
co
(
cv
x4
)
(
cv
x3
)
cmin
)
(
cv
x5
)
cexp
)
cmul
)
)
ctsu
)
)
)
)
)
.
Assume H1:
wceq
cana
(
cmpt
(
λ x0 .
cpr
cr
cc
)
(
λ x0 .
crab
(
λ x1 .
wral
(
λ x2 .
wcel
(
cv
x2
)
(
cfv
(
cdm
(
cin
(
cv
x1
)
(
co
cpnf
(
cv
x2
)
(
co
(
cv
x0
)
(
cv
x1
)
ctayl
)
)
)
)
(
cfv
(
co
(
cfv
ccnfld
ctopn
)
(
cv
x0
)
crest
)
cnt
)
)
)
(
λ x2 .
cdm
(
cv
x1
)
)
)
(
λ x1 .
co
cc
(
cv
x0
)
cpm
)
)
)
.
Assume H2:
wceq
culm
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
copab
(
λ x1 x2 .
wrex
(
λ x3 .
w3a
(
wf
(
cfv
(
cv
x3
)
cuz
)
(
co
cc
(
cv
x0
)
cmap
)
(
cv
x1
)
)
(
wf
(
cv
x0
)
cc
(
cv
x2
)
)
(
wral
(
λ x4 .
wrex
(
λ x5 .
wral
(
λ x6 .
wral
(
λ x7 .
wbr
(
cfv
(
co
(
cfv
(
cv
x7
)
(
cfv
(
cv
x6
)
(
cv
x1
)
)
)
(
cfv
(
cv
x7
)
(
cv
x2
)
)
cmin
)
cabs
)
(
cv
x4
)
clt
)
(
λ x7 .
cv
x0
)
)
...
)
...
)
...
)
)
...
)
)
)
.
...
■