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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
cram
(
cmpt2
(
λ x0 x1 .
cn0
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cinf
(
crab
(
λ x2 .
∀ x3 .
wbr
(
cv
x2
)
(
cfv
(
cv
x3
)
chash
)
cle
⟶
wral
(
λ x4 .
wrex
(
λ x5 .
wrex
(
λ x6 .
wa
(
wbr
(
cfv
(
cv
x5
)
(
cv
x1
)
)
(
cfv
(
cv
x6
)
chash
)
cle
)
(
wral
(
λ x7 .
wceq
(
cfv
(
cv
x7
)
chash
)
(
cv
x0
)
⟶
wceq
(
cfv
(
cv
x7
)
(
cv
x4
)
)
(
cv
x5
)
)
(
λ x7 .
cpw
(
cv
x6
)
)
)
)
(
λ x6 .
cpw
(
cv
x3
)
)
)
(
λ x5 .
cdm
(
cv
x1
)
)
)
(
λ x4 .
co
(
cdm
(
cv
x1
)
)
(
crab
(
λ x5 .
wceq
(
cfv
(
cv
x5
)
chash
)
(
cv
x0
)
)
(
λ x5 .
cpw
(
cv
x3
)
)
)
cmap
)
)
(
λ x2 .
cn0
)
)
cxr
clt
)
)
.
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
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.
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