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Proofgold Proof
pf
Apply df_inv__df_iso__df_cic__df_ssc__df_resc__df_subc__df_func__df_idfu__df_cofu__df_resf__df_full__df_fth__df_nat__df_fuc__df_inito__df_termo__df_zeroo__df_doma with
wceq
csubc
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cab
(
λ x1 .
wa
(
wbr
(
cv
x1
)
(
cfv
(
cv
x0
)
chomf
)
cssc
)
(
wsbc
(
λ x2 .
wral
(
λ x3 .
wa
(
wcel
(
cfv
(
cv
x3
)
(
cfv
(
cv
x0
)
ccid
)
)
(
co
(
cv
x3
)
(
cv
x3
)
(
cv
x1
)
)
)
(
wral
(
λ x4 .
wral
(
λ x5 .
wral
(
λ x6 .
wral
(
λ x7 .
wcel
(
co
(
cv
x7
)
(
cv
x6
)
(
co
(
cop
(
cv
x3
)
(
cv
x4
)
)
(
cv
x5
)
(
cfv
(
cv
x0
)
cco
)
)
)
(
co
(
cv
x3
)
(
cv
x5
)
(
cv
x1
)
)
)
(
λ x7 .
co
(
cv
x4
)
(
cv
x5
)
(
cv
x1
)
)
)
(
λ x6 .
co
(
cv
x3
)
(
cv
x4
)
(
cv
x1
)
)
)
(
λ x5 .
cv
x2
)
)
(
λ x4 .
cv
x2
)
)
)
(
λ x3 .
cv
x2
)
)
(
cdm
(
cdm
(
cv
x1
)
)
)
)
)
)
)
.
Assume H0:
wceq
cinv
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cmpt2
(
λ x1 x2 .
cfv
(
cv
x0
)
cbs
)
(
λ x1 x2 .
cfv
(
cv
x0
)
cbs
)
(
λ x1 x2 .
cin
(
co
(
cv
x1
)
(
cv
x2
)
(
cfv
(
cv
x0
)
csect
)
)
(
ccnv
(
co
(
cv
x2
)
(
cv
x1
)
(
cfv
(
cv
x0
)
csect
)
)
)
)
)
)
.
Assume H1:
wceq
ciso
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
ccom
(
cmpt
(
λ x1 .
cvv
)
(
λ x1 .
cdm
(
cv
x1
)
)
)
(
cfv
(
cv
x0
)
cinv
)
)
)
.
Assume H2:
wceq
ccic
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
co
(
cfv
(
cv
x0
)
ciso
)
c0
csupp
)
)
.
Assume H3:
wceq
cssc
(
copab
(
λ x0 x1 .
wex
(
λ x2 .
wa
(
wfn
(
cv
x1
)
(
cxp
(
cv
x2
)
(
cv
x2
)
)
)
(
wrex
(
λ x3 .
wcel
(
cv
x0
)
(
cixp
(
λ x4 .
cxp
(
cv
x3
)
(
cv
x3
)
)
(
λ x4 .
cpw
(
cfv
(
cv
x4
)
(
cv
x1
)
)
)
)
)
(
λ x3 .
cpw
(
cv
x2
)
)
)
)
)
)
.
Assume H4:
wceq
cresc
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
co
(
co
(
cv
x0
)
(
cdm
(
cdm
(
cv
x1
)
)
)
cress
)
(
cop
(
cfv
cnx
chom
)
(
cv
x1
)
)
csts
)
)
.
Assume H5:
wceq
csubc
(
cmpt
(
λ x0 .
ccat
)
(
λ x0 .
cab
(
λ x1 .
wa
(
wbr
(
cv
x1
)
(
cfv
(
cv
x0
)
chomf
)
cssc
)
(
wsbc
...
...
)
)
)
)
.
...
■