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Proofgold Proof
pf
Apply df_ec__df_qs__df_map__df_pm__df_ixp__df_en__df_dom__df_sdom__df_fin__df_fsupp__df_fi__df_sup__df_inf__df_oi__df_har__df_wdom__ax_reg__ax_inf with
∀ x0 x1 :
ι → ο
.
wceq
(
coi
x0
x1
)
(
cif
(
wa
(
wwe
x0
x1
)
(
wse
x0
x1
)
)
(
cres
(
crecs
(
cmpt
(
λ x2 .
cvv
)
(
λ x2 .
crio
(
λ x3 .
wral
(
λ x4 .
wn
(
wbr
(
cv
x4
)
(
cv
x3
)
x1
)
)
(
λ x4 .
crab
(
λ x5 .
wral
(
λ x6 .
wbr
(
cv
x6
)
(
cv
x5
)
x1
)
(
λ x6 .
crn
(
cv
x2
)
)
)
(
λ x5 .
x0
)
)
)
(
λ x3 .
crab
(
λ x4 .
wral
(
λ x5 .
wbr
(
cv
x5
)
(
cv
x4
)
x1
)
(
λ x5 .
crn
(
cv
x2
)
)
)
(
λ x4 .
x0
)
)
)
)
)
(
crab
(
λ x2 .
wrex
(
λ x3 .
wral
(
λ x4 .
wbr
(
cv
x4
)
(
cv
x3
)
x1
)
(
λ x4 .
cima
(
crecs
(
cmpt
(
λ x5 .
cvv
)
(
λ x5 .
crio
(
λ x6 .
wral
(
λ x7 .
wn
(
wbr
(
cv
x7
)
(
cv
x6
)
x1
)
)
(
λ x7 .
crab
(
λ x8 .
wral
(
λ x9 .
wbr
(
cv
x9
)
(
cv
x8
)
x1
)
(
λ x9 .
crn
(
cv
x5
)
)
)
(
λ x8 .
x0
)
)
)
(
λ x6 .
crab
(
λ x7 .
wral
(
λ x8 .
wbr
(
cv
x8
)
(
cv
x7
)
x1
)
(
λ x8 .
crn
(
cv
x5
)
)
)
(
λ x7 .
x0
)
)
)
)
)
(
cv
x2
)
)
)
(
λ x3 .
x0
)
)
(
λ x2 .
con0
)
)
)
c0
)
.
Assume H0:
∀ x0 x1 :
ι → ο
.
wceq
(
cec
x0
x1
)
(
cima
x1
(
csn
x0
)
)
.
Assume H1:
∀ x0 x1 :
ι → ο
.
wceq
(
cqs
x0
x1
)
(
cab
(
λ x2 .
wrex
(
λ x3 .
wceq
(
cv
x2
)
(
cec
(
cv
x3
)
x1
)
)
(
λ x3 .
x0
)
)
)
.
Assume H2:
wceq
cmap
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cab
(
λ x2 .
wf
(
cv
x1
)
(
cv
x0
)
(
cv
x2
)
)
)
)
.
Assume H3:
wceq
cpm
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
crab
(
λ x2 .
wfun
(
cv
x2
)
)
(
λ x2 .
cpw
(
cxp
(
cv
x1
)
(
cv
x0
)
)
)
)
)
.
Assume H4:
∀ x0 x1 :
ι →
ι → ο
.
wceq
(
cixp
(
λ x2 .
x0
x2
)
(
λ x2 .
x1
x2
)
)
(
cab
(
λ x2 .
wa
(
wfn
(
cv
x2
)
(
cab
(
λ x3 .
wcel
(
cv
x3
)
(
x0
x3
)
)
)
)
(
wral
(
λ x3 .
wcel
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
x1
x3
)
)
(
λ x3 .
x0
x3
)
)
)
)
.
Assume H5:
wceq
cen
(
copab
(
λ x0 x1 .
wex
(
λ x2 .
wf1o
(
cv
x0
)
(
cv
x1
)
(
cv
x2
)
)
)
)
.
...
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