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Proofgold Proof
pf
Apply df_cnp__df_lm__df_t0__df_t1__df_haus__df_reg__df_nrm__df_cnrm__df_pnrm__df_cmp__df_conn__df_1stc__df_2ndc__df_lly__df_nlly__df_ref__df_ptfin__df_locfin with
wceq
clocfin
(
cmpt
(
λ x0 .
ctop
)
(
λ x0 .
cab
(
λ x1 .
wa
(
wceq
(
cuni
(
cv
x0
)
)
(
cuni
(
cv
x1
)
)
)
(
wral
(
λ x2 .
wrex
(
λ x3 .
wa
(
wcel
(
cv
x2
)
(
cv
x3
)
)
(
wcel
(
crab
(
λ x4 .
wne
(
cin
(
cv
x4
)
(
cv
x3
)
)
c0
)
(
λ x4 .
cv
x1
)
)
cfn
)
)
(
λ x3 .
cv
x0
)
)
(
λ x2 .
cuni
(
cv
x0
)
)
)
)
)
)
.
Assume H0:
wceq
ccnp
(
cmpt2
(
λ x0 x1 .
ctop
)
(
λ x0 x1 .
ctop
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cuni
(
cv
x0
)
)
(
λ x2 .
crab
(
λ x3 .
wral
(
λ x4 .
wcel
(
cfv
(
cv
x2
)
(
cv
x3
)
)
(
cv
x4
)
⟶
wrex
(
λ x5 .
wa
(
wcel
(
cv
x2
)
(
cv
x5
)
)
(
wss
(
cima
(
cv
x3
)
(
cv
x5
)
)
(
cv
x4
)
)
)
(
λ x5 .
cv
x0
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
co
(
cuni
(
cv
x1
)
)
(
cuni
(
cv
x0
)
)
cmap
)
)
)
)
.
Assume H1:
wceq
clm
(
cmpt
(
λ x0 .
ctop
)
(
λ x0 .
copab
(
λ x1 x2 .
w3a
(
wcel
(
cv
x1
)
(
co
(
cuni
(
cv
x0
)
)
cc
cpm
)
)
(
wcel
(
cv
x2
)
(
cuni
(
cv
x0
)
)
)
(
wral
(
λ x3 .
wcel
(
cv
x2
)
(
cv
x3
)
⟶
wrex
(
λ x4 .
wf
(
cv
x4
)
(
cv
x3
)
(
cres
(
cv
x1
)
(
cv
x4
)
)
)
(
λ x4 .
crn
cuz
)
)
(
λ x3 .
cv
x0
)
)
)
)
)
.
Assume H2:
wceq
ct0
(
crab
(
λ x0 .
wral
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wb
(
wcel
(
cv
x1
)
(
cv
x3
)
)
(
wcel
(
cv
x2
)
(
cv
x3
)
)
)
(
λ x3 .
cv
x0
)
⟶
wceq
(
cv
x1
)
(
cv
x2
)
)
(
λ x2 .
cuni
(
cv
x0
)
)
)
(
λ x1 .
cuni
(
cv
x0
)
)
)
(
λ x0 .
ctop
)
)
.
Assume H3:
wceq
ct1
(
crab
(
λ x0 .
wral
(
λ x1 .
wcel
(
csn
(
cv
x1
)
)
(
cfv
(
cv
x0
)
ccld
)
)
(
λ x1 .
cuni
(
cv
x0
)
)
)
(
λ x0 .
ctop
)
)
.
Assume H4:
wceq
cha
(
crab
(
λ x0 .
wral
(
λ x1 .
wral
(
λ x2 .
wne
...
...
⟶
wrex
(
λ x3 .
wrex
(
λ x4 .
w3a
(
wcel
(
cv
x1
)
(
cv
x3
)
)
(
wcel
(
cv
x2
)
(
cv
x4
)
)
(
wceq
(
cin
(
cv
x3
)
(
cv
x4
)
)
c0
)
)
(
λ x4 .
cv
x0
)
)
(
λ x3 .
cv
x0
)
)
...
)
...
)
...
)
.
...
■