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Proofgold Proof
pf
Apply df_retr__df_pconn__df_sconn__df_cvm__df_goel__df_gona__df_goal__df_sat__df_sate__df_fmla__df_gonot__df_goan__df_goim__df_goor__df_gobi__df_goeq__df_goex__df_prv with
wceq
csat
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cres
(
crdg
(
cmpt
(
λ x2 .
cvv
)
(
λ x2 .
cun
(
cv
x2
)
(
copab
(
λ x3 x4 .
wrex
(
λ x5 .
wo
(
wrex
(
λ x6 .
wa
(
wceq
(
cv
x3
)
(
co
(
cfv
(
cv
x5
)
c1st
)
(
cfv
(
cv
x6
)
c1st
)
cgna
)
)
(
wceq
(
cv
x4
)
(
cdif
(
co
(
cv
x0
)
com
cmap
)
(
cin
(
cfv
(
cv
x5
)
c2nd
)
(
cfv
(
cv
x6
)
c2nd
)
)
)
)
)
(
λ x6 .
cv
x2
)
)
(
wrex
(
λ x6 .
wa
(
wceq
(
cv
x3
)
(
cgol
(
cfv
(
cv
x5
)
c1st
)
(
cv
x6
)
)
)
(
wceq
(
cv
x4
)
(
crab
(
λ x7 .
wral
(
λ x8 .
wcel
(
cun
(
csn
(
cop
(
cv
x6
)
(
cv
x8
)
)
)
(
cres
(
cv
x7
)
(
cdif
com
(
csn
(
cv
x6
)
)
)
)
)
(
cfv
(
cv
x5
)
c2nd
)
)
(
λ x8 .
cv
x0
)
)
(
λ x7 .
co
(
cv
x0
)
com
cmap
)
)
)
)
(
λ x6 .
com
)
)
)
(
λ x5 .
cv
x2
)
)
)
)
)
(
copab
(
λ x2 x3 .
wrex
(
λ x4 .
wrex
(
λ x5 .
wa
(
wceq
(
cv
x2
)
(
co
(
cv
x4
)
(
cv
x5
)
cgoe
)
)
(
wceq
(
cv
x3
)
(
crab
(
λ x6 .
wbr
(
cfv
(
cv
x4
)
(
cv
x6
)
)
(
cfv
(
cv
x5
)
(
cv
x6
)
)
(
cv
x1
)
)
(
λ x6 .
co
(
cv
x0
)
com
cmap
)
)
)
)
(
λ x5 .
com
)
)
(
λ x4 .
com
)
)
)
)
(
csuc
com
)
)
)
.
Assume H0:
wceq
cretr
(
cmpt2
(
λ x0 x1 .
ctop
)
(
λ x0 x1 .
ctop
)
(
λ x0 x1 .
crab
(
λ x2 .
wrex
(
λ x3 .
wne
(
co
(
ccom
(
cv
x2
)
(
cv
x3
)
)
(
cres
cid
(
cuni
(
cv
x0
)
)
)
(
co
(
cv
x0
)
(
cv
x0
)
chtpy
)
)
c0
)
(
λ x3 .
co
(
cv
x1
)
(
cv
x0
)
ccn
)
)
(
λ x2 .
co
(
cv
x0
)
(
cv
x1
)
ccn
)
)
)
.
Assume H1:
wceq
cpconn
(
crab
(
λ x0 .
wral
(
λ x1 .
wral
(
λ x2 .
wrex
(
λ x3 .
wa
(
wceq
(
cfv
cc0
(
cv
x3
)
)
(
cv
x1
)
)
(
wceq
(
cfv
c1
(
cv
x3
)
)
(
cv
x2
)
)
)
(
λ x3 .
co
cii
(
cv
x0
)
ccn
)
)
(
λ x2 .
cuni
(
cv
x0
)
)
)
(
λ x1 .
cuni
(
cv
x0
)
)
)
(
λ x0 .
ctop
)
)
.
Assume H2:
wceq
csconn
(
crab
(
λ x0 .
...
)
...
)
.
...
■