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Proofgold Proof
pf
Apply df_sx__df_meas__df_dde__df_ae__df_fae__df_mbfm__df_oms__df_carsg__df_sitg__df_sitm__df_itgm__df_sseq__df_fib__df_prob__df_cndprob__df_rrv__df_orvc__df_repr with
wceq
coms
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt
(
λ x1 .
cpw
(
cuni
(
cdm
(
cv
x0
)
)
)
)
(
λ x1 .
cinf
(
crn
(
cmpt
(
λ x2 .
crab
(
λ x3 .
wa
(
wss
(
cv
x1
)
(
cuni
(
cv
x3
)
)
)
(
wbr
(
cv
x3
)
com
cdom
)
)
(
λ x3 .
cpw
(
cdm
(
cv
x0
)
)
)
)
(
λ x2 .
cesum
(
λ x3 .
cv
x2
)
(
λ x3 .
cfv
(
cv
x3
)
(
cv
x0
)
)
)
)
)
(
co
cc0
cpnf
cicc
)
clt
)
)
)
.
Assume H0:
wceq
csx
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cfv
(
crn
(
cmpt2
(
λ x2 x3 .
cv
x0
)
(
λ x2 x3 .
cv
x1
)
(
λ x2 x3 .
cxp
(
cv
x2
)
(
cv
x3
)
)
)
)
csigagen
)
)
.
Assume H1:
wceq
cmeas
(
cmpt
(
λ x0 .
cuni
(
crn
csiga
)
)
(
λ x0 .
cab
(
λ x1 .
w3a
(
wf
(
cv
x0
)
(
co
cc0
cpnf
cicc
)
(
cv
x1
)
)
(
wceq
(
cfv
c0
(
cv
x1
)
)
cc0
)
(
wral
(
λ x2 .
wa
(
wbr
(
cv
x2
)
com
cdom
)
(
wdisj
(
λ x3 .
cv
x2
)
(
λ x3 .
cv
x3
)
)
⟶
wceq
(
cfv
(
cuni
(
cv
x2
)
)
(
cv
x1
)
)
(
cesum
(
λ x3 .
cv
x2
)
(
λ x3 .
cfv
(
cv
x3
)
(
cv
x1
)
)
)
)
(
λ x2 .
cpw
(
cv
x0
)
)
)
)
)
)
.
Assume H2:
wceq
cdde
(
cmpt
(
λ x0 .
cpw
cr
)
(
λ x0 .
cif
(
wcel
cc0
(
cv
x0
)
)
c1
cc0
)
)
.
Assume H3:
wceq
cae
(
copab
(
λ x0 x1 .
wceq
(
cfv
(
cdif
(
cuni
(
cdm
(
cv
x1
)
)
)
(
cv
x0
)
)
(
cv
x1
)
)
cc0
)
)
.
Assume H4:
wceq
cfae
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cuni
(
crn
cmeas
)
)
(
λ x0 x1 .
copab
(
λ x2 x3 .
wa
(
wa
(
wcel
(
cv
x2
)
(
co
(
cdm
(
cv
x0
)
)
(
cuni
(
cdm
(
cv
x1
)
)
)
cmap
)
)
(
wcel
(
cv
x3
)
(
co
(
cdm
(
cv
x0
)
)
(
cuni
(
cdm
(
cv
x1
)
)
)
cmap
)
)
)
(
wbr
(
crab
(
λ x4 .
wbr
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cv
x4
)
(
cv
x3
)
)
(
cv
x0
)
)
(
λ x4 .
cuni
(
cdm
(
cv
x1
)
)
)
)
(
cv
x1
)
cae
)
)
)
)
.
Assume H5:
wceq
cmbfm
(
cmpt2
(
λ x0 x1 .
cuni
(
crn
csiga
)
)
(
λ x0 x1 .
cuni
(
crn
csiga
)
)
(
λ x0 x1 .
crab
(
λ x2 .
wral
(
λ x3 .
wcel
(
cima
...
...
)
...
)
...
)
...
)
)
.
...
■