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Proofgold Proof
pf
Apply df_mndo__df_ghomOLD__df_rngo__df_drngo__df_rngohom__df_rngoiso__df_risc__df_com2__df_fld__df_crngo__df_idl__df_pridl__df_maxidl__df_prrngo__df_dmn__df_igen__df_xrn__df_coss with
wceq
crnghom
(
cmpt2
(
λ x0 x1 .
crngo
)
(
λ x0 x1 .
crngo
)
(
λ x0 x1 .
crab
(
λ x2 .
wa
(
wceq
(
cfv
(
cfv
(
cfv
(
cv
x0
)
c2nd
)
cgi
)
(
cv
x2
)
)
(
cfv
(
cfv
(
cv
x1
)
c2nd
)
cgi
)
)
(
wral
(
λ x3 .
wral
(
λ x4 .
wa
(
wceq
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x0
)
c1st
)
)
(
cv
x2
)
)
(
co
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cv
x1
)
c1st
)
)
)
(
wceq
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x0
)
c2nd
)
)
(
cv
x2
)
)
(
co
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cv
x1
)
c2nd
)
)
)
)
(
λ x4 .
crn
(
cfv
(
cv
x0
)
c1st
)
)
)
(
λ x3 .
crn
(
cfv
(
cv
x0
)
c1st
)
)
)
)
(
λ x2 .
co
(
crn
(
cfv
(
cv
x1
)
c1st
)
)
(
crn
(
cfv
(
cv
x0
)
c1st
)
)
cmap
)
)
)
.
Assume H0:
wceq
cmndo
(
cin
csem
cexid
)
.
Assume H1:
wceq
cghomOLD
(
cmpt2
(
λ x0 x1 .
cgr
)
(
λ x0 x1 .
cgr
)
(
λ x0 x1 .
cab
(
λ x2 .
wa
(
wf
(
crn
(
cv
x0
)
)
(
crn
(
cv
x1
)
)
(
cv
x2
)
)
(
wral
(
λ x3 .
wral
(
λ x4 .
wceq
(
co
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cv
x1
)
)
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x0
)
)
(
cv
x2
)
)
)
(
λ x4 .
crn
(
cv
x0
)
)
)
(
λ x3 .
crn
(
cv
x0
)
)
)
)
)
)
.
Assume H2:
wceq
crngo
(
copab
(
λ x0 x1 .
wa
(
wa
(
wcel
(
cv
x0
)
cablo
)
(
wf
(
cxp
(
crn
(
cv
x0
)
)
(
crn
(
cv
x0
)
)
)
(
crn
(
cv
x0
)
)
(
cv
x1
)
)
)
(
wa
(
wral
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
w3a
(
wceq
(
co
(
co
(
cv
x2
)
(
cv
x3
)
(
cv
x1
)
)
(
cv
x4
)
(
cv
x1
)
)
(
co
(
cv
x2
)
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x1
)
)
(
cv
x1
)
)
)
(
wceq
(
co
(
cv
x2
)
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x0
)
)
(
cv
x1
)
)
(
co
(
co
(
cv
x2
)
(
cv
x3
)
(
cv
x1
)
)
...
...
)
)
...
)
...
)
...
)
...
)
...
)
)
)
.
...
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