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Proofgold Proof
pf
Apply df_gim__df_gic__df_ga__df_cntz__df_cntr__df_oppg__df_symg__df_pmtr__df_psgn__df_evpm__df_od__df_gex__df_pgp__df_slw__df_lsm__df_pj1__df_efg__df_frgp with
wceq
coppg
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
co
(
cv
x0
)
(
cop
(
cfv
cnx
cplusg
)
(
ctpos
(
cfv
(
cv
x0
)
cplusg
)
)
)
csts
)
)
.
Assume H0:
wceq
cgim
(
cmpt2
(
λ x0 x1 .
cgrp
)
(
λ x0 x1 .
cgrp
)
(
λ x0 x1 .
crab
(
λ x2 .
wf1o
(
cfv
(
cv
x0
)
cbs
)
(
cfv
(
cv
x1
)
cbs
)
(
cv
x2
)
)
(
λ x2 .
co
(
cv
x0
)
(
cv
x1
)
cghm
)
)
)
.
Assume H1:
wceq
cgic
(
cima
(
ccnv
cgim
)
(
cdif
cvv
c1o
)
)
.
Assume H2:
wceq
cga
(
cmpt2
(
λ x0 x1 .
cgrp
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
csb
(
cfv
(
cv
x0
)
cbs
)
(
λ x2 .
crab
(
λ x3 .
wral
(
λ x4 .
wa
(
wceq
(
co
(
cfv
(
cv
x0
)
c0g
)
(
cv
x4
)
(
cv
x3
)
)
(
cv
x4
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wceq
(
co
(
co
(
cv
x5
)
(
cv
x6
)
(
cfv
(
cv
x0
)
cplusg
)
)
(
cv
x4
)
(
cv
x3
)
)
(
co
(
cv
x5
)
(
co
(
cv
x6
)
(
cv
x4
)
(
cv
x3
)
)
(
cv
x3
)
)
)
(
λ x6 .
cv
x2
)
)
(
λ x5 .
cv
x2
)
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
co
(
cv
x1
)
(
cxp
(
cv
x2
)
(
cv
x1
)
)
cmap
)
)
)
)
.
Assume H3:
wceq
ccntz
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt
(
λ x1 .
cpw
(
cfv
(
cv
x0
)
cbs
)
)
(
λ x1 .
crab
(
λ x2 .
wral
(
λ x3 .
wceq
(
co
(
cv
x2
)
(
cv
x3
)
(
cfv
(
cv
x0
)
cplusg
)
)
(
co
(
cv
x3
)
(
cv
x2
)
(
cfv
(
cv
x0
)
cplusg
)
)
)
(
λ x3 .
cv
x1
)
)
(
λ x2 .
cfv
(
cv
x0
)
cbs
)
)
)
)
.
Assume H4:
wceq
ccntr
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cfv
(
cfv
(
cv
x0
)
cbs
)
(
cfv
(
cv
x0
)
ccntz
)
)
)
.
Assume H5:
wceq
coppg
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
co
(
cv
x0
)
(
cop
(
cfv
cnx
cplusg
)
(
ctpos
(
cfv
(
cv
x0
)
cplusg
)
)
)
csts
)
)
.
Assume H6:
wceq
csymg
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
csb
(
cab
(
λ x1 .
wf1o
(
cv
x0
)
(
cv
x0
)
(
cv
x1
)
)
)
(
λ x1 .
ctp
(
cop
(
cfv
cnx
cbs
)
(
cv
x1
)
)
(
cop
(
cfv
cnx
cplusg
)
(
cmpt2
(
λ x2 x3 .
cv
x1
)
(
λ x2 x3 .
...
)
...
)
)
...
)
)
)
.
...
■