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Proofgold Proof
pf
Apply df_minmar1__df_cpmat__df_mat2pmat__df_cpmat2mat__df_decpmat__df_pm2mp__df_chpmat__df_top__df_topon__df_topsp__df_bases__df_cld__df_ntr__df_cls__df_nei__df_lp__df_perf__df_cn with
wceq
cchpmat
(
cmpt2
(
λ x0 x1 .
cfn
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cfv
(
co
(
cv
x0
)
(
cv
x1
)
cmat
)
cbs
)
(
λ x2 .
cfv
(
co
(
co
(
cfv
(
cv
x1
)
cv1
)
(
cfv
(
co
(
cv
x0
)
(
cfv
(
cv
x1
)
cpl1
)
cmat
)
cur
)
(
cfv
(
co
(
cv
x0
)
(
cfv
(
cv
x1
)
cpl1
)
cmat
)
cvsca
)
)
(
cfv
(
cv
x2
)
(
co
(
cv
x0
)
(
cv
x1
)
cmat2pmat
)
)
(
cfv
(
co
(
cv
x0
)
(
cfv
(
cv
x1
)
cpl1
)
cmat
)
csg
)
)
(
co
(
cv
x0
)
(
cfv
(
cv
x1
)
cpl1
)
cmdat
)
)
)
)
.
Assume H0:
wceq
cminmar1
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cfv
(
co
(
cv
x0
)
(
cv
x1
)
cmat
)
cbs
)
(
λ x2 .
cmpt2
(
λ x3 x4 .
cv
x0
)
(
λ x3 x4 .
cv
x0
)
(
λ x3 x4 .
cmpt2
(
λ x5 x6 .
cv
x0
)
(
λ x5 x6 .
cv
x0
)
(
λ x5 x6 .
cif
(
wceq
(
cv
x5
)
(
cv
x3
)
)
(
cif
(
wceq
(
cv
x6
)
(
cv
x4
)
)
(
cfv
(
cv
x1
)
cur
)
(
cfv
(
cv
x1
)
c0g
)
)
(
co
(
cv
x5
)
(
cv
x6
)
(
cv
x2
)
)
)
)
)
)
)
.
Assume H1:
wceq
ccpmat
(
cmpt2
(
λ x0 x1 .
cfn
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
crab
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wral
(
λ x5 .
wceq
(
cfv
(
cv
x5
)
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
cco1
)
)
(
cfv
(
cv
x1
)
c0g
)
)
(
λ x5 .
cn
)
)
(
λ x4 .
cv
x0
)
)
(
λ x3 .
cv
x0
)
)
(
λ x2 .
cfv
(
co
(
cv
x0
)
(
cfv
(
cv
x1
)
cpl1
)
cmat
)
cbs
)
)
)
.
Assume H2:
wceq
cmat2pmat
(
cmpt2
(
λ x0 x1 .
cfn
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cfv
(
co
(
cv
x0
)
(
cv
x1
)
cmat
)
cbs
)
(
λ x2 .
cmpt2
(
λ x3 x4 .
cv
x0
)
(
λ x3 x4 .
cv
x0
)
(
λ x3 x4 .
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cfv
(
cv
x1
)
cpl1
)
cascl
)
)
)
)
)
.
Assume H3:
wceq
ccpmat2mat
(
cmpt2
(
λ x0 x1 .
cfn
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cmpt
(
λ x2 .
co
(
cv
x0
)
(
cv
x1
)
ccpmat
)
(
λ x2 .
cmpt2
(
λ x3 x4 .
cv
x0
)
...
...
)
)
)
.
...
■