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Proofgold Proof
pf
Apply df_gzext__df_gzrep__df_gzpow__df_gzun__df_gzreg__df_gzinf__df_gzf__df_mcn__df_mvar__df_mty__df_mtc__df_mmax__df_mvt__df_mrex__df_mex__df_mdv__df_mvrs__df_mrsub with
wceq
cmtc
(
cslot
c4
)
.
Assume H0:
wceq
cgze
(
co
(
cgol
(
co
(
co
c2o
c0
cgoe
)
(
co
c2o
c1o
cgoe
)
cgob
)
c2o
)
(
co
c0
c1o
cgoq
)
cgoi
)
.
Assume H1:
wceq
cgzr
(
cmpt
(
λ x0 .
cfv
com
cfmla
)
(
λ x0 .
co
(
cgol
(
cgox
(
cgol
(
co
(
cgol
(
cv
x0
)
c1o
)
(
co
c2o
c1o
cgoq
)
cgoi
)
c2o
)
c1o
)
c3o
)
(
cgol
(
cgol
(
co
(
co
c2o
c1o
cgoe
)
(
cgox
(
co
(
co
c3o
c0
cgoe
)
(
cgol
(
cv
x0
)
c1o
)
cgoa
)
c3o
)
cgob
)
c2o
)
c1o
)
cgoi
)
)
.
Assume H2:
wceq
cgzp
(
cgox
(
cgol
(
co
(
cgol
(
co
(
co
c1o
c2o
cgoe
)
(
co
c1o
c0
cgoe
)
cgob
)
c1o
)
(
co
c2o
c1o
cgoe
)
cgoi
)
c2o
)
c1o
)
.
Assume H3:
wceq
cgzu
(
cgox
(
cgol
(
co
(
cgox
(
co
(
co
c2o
c1o
cgoe
)
(
co
c1o
c0
cgoe
)
cgoa
)
c1o
)
(
co
c2o
c1o
cgoe
)
cgoi
)
c2o
)
c1o
)
.
Assume H4:
wceq
cgzg
(
co
(
cgox
(
co
c1o
c0
cgoe
)
c1o
)
(
cgox
(
co
(
co
c1o
c0
cgoe
)
(
cgol
(
co
(
co
c2o
c1o
cgoe
)
(
cgon
(
co
c2o
c0
cgoe
)
)
cgoi
)
c2o
)
cgoa
)
c1o
)
cgoi
)
.
Assume H5:
wceq
cgzi
(
cgox
(
co
(
co
c0
c1o
cgoe
)
(
cgol
(
co
(
co
c2o
c1o
cgoe
)
(
cgox
(
co
(
co
c2o
c0
cgoe
)
(
co
c0
c1o
cgoe
)
cgoa
)
c0
)
cgoi
)
c2o
)
cgoa
)
c1o
)
.
Assume H6:
wceq
cgzf
(
cab
(
λ x0 .
w3a
(
w3a
(
wtr
(
cv
x0
)
)
(
wbr
(
cv
x0
)
cgze
cprv
)
(
wbr
(
cv
x0
)
cgzp
cprv
)
)
(
w3a
(
wbr
(
cv
x0
)
cgzu
cprv
)
(
wbr
(
cv
x0
)
cgzg
cprv
)
(
wbr
(
cv
x0
)
cgzi
cprv
)
)
(
wral
(
λ x1 .
wbr
(
cv
x0
)
(
cfv
(
cv
x1
)
cgzr
)
cprv
)
(
λ x1 .
cfv
com
cfmla
)
)
)
)
.
Assume H7:
wceq
cmcn
(
cslot
c1
)
.
Assume H8:
wceq
cmvar
(
cslot
c2
)
.
Assume H9:
wceq
cmty
(
cslot
c3
)
.
Assume H10:
wceq
cmtc
(
cslot
...
)
.
...
■