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Proofgold Proof
pf
Apply df_mpl__df_ltbag__df_opsr__df_evls__df_evl__df_mhp__df_psd__df_selv__df_algind__df_psr1__df_vr1__df_ply1__df_coe1__df_toply1__df_evls1__df_evl1__df_psmet__df_xmet with
wceq
cpsmet
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
crab
(
λ x1 .
wral
(
λ x2 .
wa
(
wceq
(
co
(
cv
x2
)
(
cv
x2
)
(
cv
x1
)
)
cc0
)
(
wral
(
λ x3 .
wral
(
λ x4 .
wbr
(
co
(
cv
x2
)
(
cv
x3
)
(
cv
x1
)
)
(
co
(
co
(
cv
x4
)
(
cv
x2
)
(
cv
x1
)
)
(
co
(
cv
x4
)
(
cv
x3
)
(
cv
x1
)
)
cxad
)
cle
)
(
λ x4 .
cv
x0
)
)
(
λ x3 .
cv
x0
)
)
)
(
λ x2 .
cv
x0
)
)
(
λ x1 .
co
cxr
(
cxp
(
cv
x0
)
(
cv
x0
)
)
cmap
)
)
)
.
Assume H0:
wceq
cmpl
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
csb
(
co
(
cv
x0
)
(
cv
x1
)
cmps
)
(
λ x2 .
co
(
cv
x2
)
(
crab
(
λ x3 .
wbr
(
cv
x3
)
(
cfv
(
cv
x1
)
c0g
)
cfsupp
)
(
λ x3 .
cfv
(
cv
x2
)
cbs
)
)
cress
)
)
)
.
Assume H1:
wceq
cltb
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
copab
(
λ x2 x3 .
wa
(
wss
(
cpr
(
cv
x2
)
(
cv
x3
)
)
(
crab
(
λ x4 .
wcel
(
cima
(
ccnv
(
cv
x4
)
)
cn
)
cfn
)
(
λ x4 .
co
cn0
(
cv
x1
)
cmap
)
)
)
(
wrex
(
λ x4 .
wa
(
wbr
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cv
x4
)
(
cv
x3
)
)
clt
)
(
wral
(
λ x5 .
wbr
(
cv
x4
)
(
cv
x5
)
(
cv
x0
)
⟶
wceq
(
cfv
(
cv
x5
)
(
cv
x2
)
)
(
cfv
(
cv
x5
)
(
cv
x3
)
)
)
(
λ x5 .
cv
x1
)
)
)
(
λ x4 .
cv
x1
)
)
)
)
)
.
Assume H2:
wceq
copws
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cpw
(
cxp
(
cv
x0
)
(
cv
x0
)
)
)
(
λ x2 .
csb
(
co
(
cv
x0
)
(
cv
x1
)
cmps
)
(
λ x3 .
co
(
cv
x3
)
(
cop
(
cfv
cnx
cple
)
(
copab
(
λ x4 x5 .
wa
(
wss
(
cpr
(
cv
x4
)
(
cv
x5
)
)
(
cfv
(
cv
x3
)
cbs
)
)
(
wo
(
wsbc
(
λ x6 .
wrex
(
λ x7 .
wa
(
wbr
(
cfv
(
cv
x7
)
(
cv
x4
)
)
(
cfv
(
cv
x7
)
(
cv
x5
)
)
(
cfv
(
cv
x1
)
cplt
)
)
(
wral
(
λ x8 .
...
⟶
wceq
(
cfv
(
cv
x8
)
(
cv
x4
)
)
(
cfv
(
cv
x8
)
...
)
)
...
)
)
...
)
...
)
...
)
)
)
)
...
)
)
)
)
.
...
■