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Proofgold Proof
pf
Apply df_preset__df_drs__df_poset__df_plt__df_lub__df_glb__df_join__df_meet__df_toset__df_p0__df_p1__df_lat__df_clat__df_odu__df_ipo__df_dlat__df_ps__df_tsr with
wceq
cp1
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cfv
(
cfv
(
cv
x0
)
cbs
)
(
cfv
(
cv
x0
)
club
)
)
)
.
Assume H0:
wceq
cpreset
(
cab
(
λ x0 .
wsbc
(
λ x1 .
wsbc
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wral
(
λ x5 .
wa
(
wbr
(
cv
x3
)
(
cv
x3
)
(
cv
x2
)
)
(
wa
(
wbr
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
wbr
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
⟶
wbr
(
cv
x3
)
(
cv
x5
)
(
cv
x2
)
)
)
(
λ x5 .
cv
x1
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cv
x1
)
)
(
cfv
(
cv
x0
)
cple
)
)
(
cfv
(
cv
x0
)
cbs
)
)
)
.
Assume H1:
wceq
cdrs
(
crab
(
λ x0 .
wsbc
(
λ x1 .
wsbc
(
λ x2 .
wa
(
wne
(
cv
x1
)
c0
)
(
wral
(
λ x3 .
wral
(
λ x4 .
wrex
(
λ x5 .
wa
(
wbr
(
cv
x3
)
(
cv
x5
)
(
cv
x2
)
)
(
wbr
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
)
(
λ x5 .
cv
x1
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cv
x1
)
)
)
(
cfv
(
cv
x0
)
cple
)
)
(
cfv
(
cv
x0
)
cbs
)
)
(
λ x0 .
cpreset
)
)
.
Assume H2:
wceq
cpo
(
cab
(
λ x0 .
wex
(
λ x1 .
wex
(
λ x2 .
w3a
(
wceq
(
cv
x1
)
(
cfv
(
cv
x0
)
cbs
)
)
(
wceq
(
cv
x2
)
(
cfv
(
cv
x0
)
cple
)
)
(
wral
(
λ x3 .
wral
(
λ x4 .
wral
(
λ x5 .
w3a
(
wbr
(
cv
x3
)
(
cv
x3
)
(
cv
x2
)
)
(
wa
(
wbr
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
wbr
(
cv
x4
)
(
cv
x3
)
(
cv
x2
)
)
⟶
wceq
(
cv
x3
)
(
cv
x4
)
)
(
wa
(
wbr
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
wbr
(
cv
x4
)
(
cv
x5
)
(
cv
x2
)
)
⟶
wbr
(
cv
x3
)
(
cv
x5
)
(
cv
x2
)
)
)
(
λ x5 .
cv
x1
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cv
x1
)
)
)
)
)
)
.
Assume H3:
wceq
cplt
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cdif
(
cfv
(
cv
x0
)
cple
)
cid
)
)
.
Assume H4:
wceq
club
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cres
(
cmpt
(
λ x1 .
cpw
(
cfv
(
cv
x0
)
cbs
)
)
(
λ x1 .
crio
(
λ x2 .
wa
(
wral
(
λ x3 .
wbr
...
...
...
)
...
)
...
)
...
)
)
...
)
)
.
...
■