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Proofgold Proof
pf
Apply df_vts__ax_hgt749__ax_ros335__ax_ros336__df_trkg2d__df_afs__df_bnj17__df_bnj14__df_bnj13__df_bnj15__df_bnj18__df_bnj19__ax_7d__ax_8d__ax_9d1__ax_9d2__ax_10d__ax_11d with
∀ x0 .
wn
(
∀ x1 .
wn
(
wceq
(
cv
x1
)
(
cv
x0
)
)
)
.
Assume H0:
wceq
cvts
(
cmpt2
(
λ x0 x1 .
co
cc
cn
cmap
)
(
λ x0 x1 .
cn0
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cc
)
(
λ x2 .
csu
(
co
c1
(
cv
x1
)
cfz
)
(
λ x3 .
co
(
cfv
(
cv
x3
)
(
cv
x0
)
)
(
cfv
(
co
(
co
ci
(
co
c2
cpi
cmul
)
cmul
)
(
co
(
cv
x3
)
(
cv
x2
)
cmul
)
cmul
)
ce
)
cmul
)
)
)
)
.
Assume H1:
wral
(
λ x0 .
wbr
(
co
(
cdc
c1
cc0
)
(
cdc
c2
c7
)
cexp
)
(
cv
x0
)
cle
⟶
wrex
(
λ x1 .
wrex
(
λ x2 .
w3a
(
wral
(
λ x3 .
wbr
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
co
c1
(
cdp2
cc0
(
cdp2
c7
(
cdp2
c9
(
cdp2
c9
(
cdp2
c5
c5
)
)
)
)
)
cdp
)
cle
)
(
λ x3 .
cn
)
)
(
wral
(
λ x3 .
wbr
(
cfv
(
cv
x3
)
(
cv
x1
)
)
(
co
c1
(
cdp2
c4
(
cdp2
c1
c4
)
)
cdp
)
cle
)
(
λ x3 .
cn
)
)
(
wbr
(
co
(
co
cc0
(
cdp2
cc0
(
cdp2
cc0
(
cdp2
cc0
(
cdp2
c4
(
cdp2
c2
(
cdp2
c2
(
cdp2
c4
c8
)
)
)
)
)
)
)
cdp
)
(
co
(
cv
x0
)
c2
cexp
)
cmul
)
(
citg
(
λ x3 .
co
cc0
c1
cioo
)
(
λ x3 .
co
(
co
(
cfv
(
cv
x3
)
(
co
(
co
cvma
(
cv
x1
)
(
cof
cmul
)
)
(
cv
x0
)
cvts
)
)
(
co
(
cfv
(
cv
x3
)
(
co
(
co
cvma
(
cv
x2
)
(
cof
cmul
)
)
(
cv
x0
)
cvts
)
)
c2
cexp
)
cmul
)
(
cfv
(
co
(
co
ci
(
co
c2
cpi
cmul
)
cmul
)
(
co
(
cneg
(
cv
x0
)
)
(
cv
x3
)
cmul
)
cmul
)
ce
)
cmul
)
)
cle
)
)
(
λ x2 .
co
(
co
cc0
cpnf
cico
)
cn
cmap
)
)
(
λ x1 .
co
(
co
cc0
cpnf
cico
)
cn
cmap
)
)
(
λ x0 .
crab
(
λ x1 .
wn
(
wbr
c2
(
cv
x1
)
cdvds
)
)
(
λ x1 .
cz
)
)
.
Assume H2:
wral
(
λ x0 .
wbr
(
cfv
(
cv
x0
)
cchp
)
(
co
(
co
c1
(
cdp2
cc0
(
cdp2
c3
(
cdp2
c8
(
cdp2
c8
c3
)
)
)
)
...
)
...
...
)
...
)
...
.
...
■