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Proofgold Proof
pf
Apply df_odz__df_phi__df_pc__df_gz__df_vdwap__df_vdwmc__df_vdwpc__df_ram__df_prmo__df_struct__df_ndx__df_slot__df_base__df_sets__df_ress__df_plusg__df_mulr__df_starv with
wceq
cnx
(
cres
cid
cn
)
.
Assume H0:
wceq
codz
(
cmpt
(
λ x0 .
cn
)
(
λ x0 .
cmpt
(
λ x1 .
crab
(
λ x2 .
wceq
(
co
(
cv
x2
)
(
cv
x0
)
cgcd
)
c1
)
(
λ x2 .
cz
)
)
(
λ x1 .
cinf
(
crab
(
λ x2 .
wbr
(
cv
x0
)
(
co
(
co
(
cv
x1
)
(
cv
x2
)
cexp
)
c1
cmin
)
cdvds
)
(
λ x2 .
cn
)
)
cr
clt
)
)
)
.
Assume H1:
wceq
cphi
(
cmpt
(
λ x0 .
cn
)
(
λ x0 .
cfv
(
crab
(
λ x1 .
wceq
(
co
(
cv
x1
)
(
cv
x0
)
cgcd
)
c1
)
(
λ x1 .
co
c1
(
cv
x0
)
cfz
)
)
chash
)
)
.
Assume H2:
wceq
cpc
(
cmpt2
(
λ x0 x1 .
cprime
)
(
λ x0 x1 .
cq
)
(
λ x0 x1 .
cif
(
wceq
(
cv
x1
)
cc0
)
cpnf
(
cio
(
λ x2 .
wrex
(
λ x3 .
wrex
(
λ x4 .
wa
(
wceq
(
cv
x1
)
(
co
(
cv
x3
)
(
cv
x4
)
cdiv
)
)
(
wceq
(
cv
x2
)
(
co
(
csup
(
crab
(
λ x5 .
wbr
(
co
(
cv
x0
)
(
cv
x5
)
cexp
)
(
cv
x3
)
cdvds
)
(
λ x5 .
cn0
)
)
cr
clt
)
(
csup
(
crab
(
λ x5 .
wbr
(
co
(
cv
x0
)
(
cv
x5
)
cexp
)
(
cv
x4
)
cdvds
)
(
λ x5 .
cn0
)
)
cr
clt
)
cmin
)
)
)
(
λ x4 .
cn
)
)
(
λ x3 .
cz
)
)
)
)
)
.
Assume H3:
wceq
cgz
(
crab
(
λ x0 .
wa
(
wcel
(
cfv
(
cv
x0
)
cre
)
cz
)
(
wcel
(
cfv
(
cv
x0
)
cim
)
cz
)
)
(
λ x0 .
cc
)
)
.
Assume H4:
wceq
cvdwa
(
cmpt
(
λ x0 .
cn0
)
(
λ x0 .
cmpt2
(
λ x1 x2 .
cn
)
(
λ x1 x2 .
cn
)
(
λ x1 x2 .
crn
(
cmpt
(
λ x3 .
co
cc0
(
co
(
cv
x0
)
c1
cmin
)
cfz
)
(
λ x3 .
co
(
cv
x1
)
(
co
(
cv
x3
)
(
cv
x2
)
cmul
)
caddc
)
)
)
)
)
.
Assume H5:
wceq
cvdwm
(
copab
(
λ x0 x1 .
wex
(
λ x2 .
wne
(
cin
(
crn
(
cfv
(
cv
x0
)
cvdwa
)
)
(
cpw
(
cima
(
ccnv
(
cv
x1
)
)
(
csn
(
cv
x2
)
)
)
)
)
c0
)
)
)
.
Assume H6:
wceq
cvdwp
(
coprab
(
λ x0 x1 x2 .
wrex
(
λ x3 .
wrex
(
λ x4 .
wa
(
wral
(
λ x5 .
wss
(
co
(
co
(
cv
x3
)
(
cfv
(
cv
x5
)
(
cv
x4
)
)
caddc
)
(
cfv
(
cv
x5
)
(
cv
x4
)
)
(
cfv
(
cv
x1
)
cvdwa
)
)
...
)
...
)
...
)
...
)
...
)
)
.
...
■