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Proofgold Proof
pf
Apply df_rnghom__df_rngiso__df_ric__df_drng__df_field__df_subrg__df_rgspn__df_abv__df_staf__df_srng__df_lmod__df_scaf__df_lss__df_lsp__df_lmhm__df_lmim__df_lmic__df_lbs with
wceq
clmic
(
cima
(
ccnv
clmim
)
(
cdif
cvv
c1o
)
)
.
Assume H0:
wceq
crh
(
cmpt2
(
λ x0 x1 .
crg
)
(
λ x0 x1 .
crg
)
(
λ x0 x1 .
csb
(
cfv
(
cv
x0
)
cbs
)
(
λ x2 .
csb
(
cfv
(
cv
x1
)
cbs
)
(
λ x3 .
crab
(
λ x4 .
wa
(
wceq
(
cfv
(
cfv
(
cv
x0
)
cur
)
(
cv
x4
)
)
(
cfv
(
cv
x1
)
cur
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wa
(
wceq
(
cfv
(
co
(
cv
x5
)
(
cv
x6
)
(
cfv
(
cv
x0
)
cplusg
)
)
(
cv
x4
)
)
(
co
(
cfv
(
cv
x5
)
(
cv
x4
)
)
(
cfv
(
cv
x6
)
(
cv
x4
)
)
(
cfv
(
cv
x1
)
cplusg
)
)
)
(
wceq
(
cfv
(
co
(
cv
x5
)
(
cv
x6
)
(
cfv
(
cv
x0
)
cmulr
)
)
(
cv
x4
)
)
(
co
(
cfv
(
cv
x5
)
(
cv
x4
)
)
(
cfv
(
cv
x6
)
(
cv
x4
)
)
(
cfv
(
cv
x1
)
cmulr
)
)
)
)
(
λ x6 .
cv
x2
)
)
(
λ x5 .
cv
x2
)
)
)
(
λ x4 .
co
(
cv
x3
)
(
cv
x2
)
cmap
)
)
)
)
)
.
Assume H1:
wceq
crs
(
cmpt2
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
cvv
)
(
λ x0 x1 .
crab
(
λ x2 .
wcel
(
ccnv
(
cv
x2
)
)
(
co
(
cv
x1
)
(
cv
x0
)
crh
)
)
(
λ x2 .
co
(
cv
x0
)
(
cv
x1
)
crh
)
)
)
.
Assume H2:
wceq
cric
(
cima
(
ccnv
crs
)
(
cdif
cvv
c1o
)
)
.
Assume H3:
wceq
cdr
(
crab
(
λ x0 .
wceq
(
cfv
(
cv
x0
)
cui
)
(
cdif
(
cfv
(
cv
x0
)
cbs
)
(
csn
(
cfv
(
cv
x0
)
c0g
)
)
)
)
(
λ x0 .
crg
)
)
.
Assume H4:
wceq
cfield
(
cin
cdr
ccrg
)
.
Assume H5:
wceq
csubrg
(
cmpt
(
λ x0 .
crg
)
(
λ x0 .
crab
(
λ x1 .
wa
(
wcel
(
co
(
cv
x0
)
(
cv
x1
)
cress
)
crg
)
(
wcel
(
cfv
(
cv
x0
)
cur
)
(
cv
x1
)
)
)
(
λ x1 .
cpw
(
cfv
(
cv
x0
)
cbs
)
)
)
)
.
Assume H6:
wceq
crgspn
(
cmpt
(
λ x0 .
cvv
)
(
λ x0 .
cmpt
(
λ x1 .
cpw
(
cfv
(
cv
x0
)
cbs
)
)
(
λ x1 .
cint
(
crab
(
λ x2 .
wss
(
cv
x1
)
(
cv
x2
)
)
(
λ x2 .
cfv
(
cv
x0
)
csubrg
)
)
)
)
)
.
Assume H7:
wceq
cabv
(
cmpt
(
λ x0 .
crg
)
(
λ x0 .
crab
(
λ x1 .
wral
(
λ x2 .
wa
(
wb
(
wceq
...
...
)
...
)
...
)
...
)
...
)
)
.
...
■