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Proofgold Proof
pf
Apply df_msub__df_mvh__df_mpst__df_msr__df_msta__df_mfs__df_mcls__df_mpps__df_mthm__df_m0s__df_msa__df_mwgfs__df_msyn__df_mtree__df_mst__df_msax__df_mufs__df_muv with
wceq
cmcls
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt2
(
λ x1 x2 .
cpw
(
cfv
(
cv
x0
)
cmdv
)
)
(
λ x1 x2 .
cpw
(
cfv
(
cv
x0
)
cmex
)
)
(
λ x1 x2 .
cint
(
cab
(
λ x3 .
wa
(
wss
(
cun
(
cv
x2
)
(
crn
(
cfv
(
cv
x0
)
cmvh
)
)
)
(
cv
x3
)
)
(
∀ x4 x5 x6 .
wcel
(
cotp
(
cv
x4
)
(
cv
x5
)
(
cv
x6
)
)
(
cfv
(
cv
x0
)
cmax
)
⟶
wral
(
λ x7 .
wa
(
wss
(
cima
(
cv
x7
)
(
cun
(
cv
x5
)
(
crn
(
cfv
(
cv
x0
)
cmvh
)
)
)
)
(
cv
x3
)
)
(
∀ x8 x9 .
wbr
(
cv
x8
)
(
cv
x9
)
(
cv
x4
)
⟶
wss
(
cxp
(
cfv
(
cfv
(
cfv
(
cv
x8
)
(
cfv
(
cv
x0
)
cmvh
)
)
(
cv
x7
)
)
(
cfv
(
cv
x0
)
cmvrs
)
)
(
cfv
(
cfv
(
cfv
(
cv
x9
)
(
cfv
(
cv
x0
)
cmvh
)
)
(
cv
x7
)
)
(
cfv
(
cv
x0
)
cmvrs
)
)
)
(
cv
x1
)
)
⟶
wcel
(
cfv
(
cv
x6
)
(
cv
x7
)
)
(
cv
x3
)
)
(
λ x7 .
crn
(
cfv
(
cv
x0
)
cmsub
)
)
)
)
)
)
)
)
.
Assume H0:
wceq
cmsub
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt
(
λ x1 .
co
(
cfv
(
cv
x0
)
cmrex
)
(
cfv
(
cv
x0
)
cmvar
)
cpm
)
(
λ x1 .
cmpt
(
λ x2 .
cfv
(
cv
x0
)
cmex
)
(
λ x2 .
cop
(
cfv
(
cv
x2
)
c1st
)
(
cfv
(
cfv
(
cv
x2
)
c2nd
)
(
cfv
(
cv
x1
)
(
cfv
(
cv
x0
)
cmrsub
)
)
)
)
)
)
)
.
Assume H1:
wceq
cmvh
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt
(
λ x1 .
cfv
(
cv
x0
)
cmvar
)
(
λ x1 .
cop
(
cfv
(
cv
x1
)
(
cfv
(
cv
x0
)
cmty
)
)
(
cs1
(
cv
x1
)
)
)
)
)
.
Assume H2:
wceq
cmpst
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cxp
(
cxp
(
crab
(
λ x1 .
wceq
(
ccnv
(
cv
x1
)
)
(
cv
x1
)
)
(
λ x1 .
cpw
(
cfv
(
cv
x0
)
cmdv
)
)
)
(
cin
(
cpw
(
cfv
(
cv
x0
)
cmex
)
)
cfn
)
)
(
cfv
(
cv
x0
)
cmex
)
)
)
.
Assume H3:
wceq
cmsr
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt
(
λ x1 .
cfv
(
cv
x0
)
cmpst
)
(
λ x1 .
csb
(
cfv
(
cfv
(
cv
x1
)
c1st
)
c2nd
)
(
λ x2 .
csb
(
cfv
(
cv
x1
)
c2nd
)
(
λ x3 .
cotp
(
cin
...
...
)
...
...
)
)
)
)
)
.
...
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