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Proofgold Proof
pf
Apply df_supp__df_tpos__df_cur__df_unc__df_undef__df_wrecs__df_smo__df_recs__df_rdg__df_seqom__df_1o__df_2o__df_3o__df_4o__df_oadd__df_omul__df_oexp__df_er with
wceq
c3o
(
csuc
c2o
)
.
Assume H0:
wceq
csupp
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
crab
(
λ x2 .
wne
(
cima
(
cv
x0
)
(
csn
(
cv
x2
)
)
)
(
csn
(
cv
x1
)
)
)
(
λ x2 .
cdm
(
cv
x0
)
)
)
)
.
Assume H1:
∀ x0 :
ι → ο
.
wceq
(
ctpos
x0
)
(
ccom
x0
(
cmpt
(
λ x1 .
cun
(
ccnv
(
cdm
x0
)
)
(
csn
c0
)
)
(
λ x1 .
cuni
(
ccnv
(
csn
(
cv
x1
)
)
)
)
)
)
.
Assume H2:
∀ x0 :
ι → ο
.
wceq
(
ccur
x0
)
(
cmpt
(
λ x1 .
cdm
(
cdm
x0
)
)
(
λ x1 .
copab
(
λ x2 x3 .
wbr
(
cop
(
cv
x1
)
(
cv
x2
)
)
(
cv
x3
)
x0
)
)
)
.
Assume H3:
∀ x0 :
ι → ο
.
wceq
(
cunc
x0
)
(
coprab
(
λ x1 x2 x3 .
wbr
(
cv
x2
)
(
cv
x3
)
(
cfv
(
cv
x1
)
x0
)
)
)
.
Assume H4:
wceq
cund
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cpw
(
cuni
(
cv
x0
)
)
)
)
.
Assume H5:
∀ x0 x1 x2 :
ι → ο
.
wceq
(
cwrecs
x0
x1
x2
)
(
cuni
(
cab
(
λ x3 .
wex
(
λ x4 .
w3a
(
wfn
(
cv
x3
)
(
cv
x4
)
)
(
wa
(
wss
(
cv
x4
)
x0
)
(
wral
(
λ x5 .
wss
(
cpred
x0
x1
(
cv
x5
)
)
(
cv
x4
)
)
(
λ x5 .
cv
x4
)
)
)
(
wral
(
λ x5 .
wceq
(
cfv
(
cv
x5
)
(
cv
x3
)
)
(
cfv
(
cres
(
cv
x3
)
(
cpred
x0
x1
(
cv
x5
)
)
)
x2
)
)
(
λ x5 .
cv
x4
)
)
)
)
)
)
.
Assume H6:
∀ x0 :
ι → ο
.
wb
(
wsmo
x0
)
(
w3a
(
wf
(
cdm
x0
)
con0
x0
)
(
word
(
cdm
x0
)
)
(
wral
(
λ x1 .
wral
(
λ x2 .
wcel
(
cv
x1
)
(
cv
x2
)
⟶
wcel
(
cfv
(
cv
x1
)
x0
)
(
cfv
(
cv
x2
)
x0
)
)
(
λ x2 .
cdm
x0
)
)
(
λ x1 .
cdm
x0
)
)
)
.
Assume H7:
∀ x0 :
ι → ο
.
wceq
(
crecs
x0
)
(
cwrecs
con0
cep
x0
)
.
Assume H8:
∀ x0 x1 :
ι → ο
.
wceq
(
crdg
x0
x1
)
(
crecs
(
cmpt
(
λ x2 .
cvv
)
(
λ x2 .
cif
(
wceq
(
cv
x2
)
c0
)
x1
(
cif
(
wlim
(
cdm
(
cv
x2
)
)
)
(
cuni
(
crn
(
cv
x2
)
)
)
(
cfv
(
cfv
(
cuni
(
cdm
(
cv
x2
)
)
)
(
cv
x2
)
)
x0
)
)
)
)
)
.
Assume H9:
∀ x0 x1 :
ι → ο
.
wceq
(
cseqom
x0
x1
)
(
cima
(
crdg
(
cmpt2
(
λ x2 x3 .
com
)
(
λ x2 x3 .
cvv
)
(
λ x2 x3 .
cop
(
csuc
(
cv
x2
)
)
...
)
)
...
)
...
)
.
...
■