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Proofgold Proposition
∀ x0 : ο .
(
wceq
cvts
(
cmpt2
(
λ x1 x2 .
co
cc
cn
cmap
)
(
λ x1 x2 .
cn0
)
(
λ x1 x2 .
cmpt
(
λ x3 .
cc
)
(
λ x3 .
csu
(
co
c1
(
cv
x2
)
cfz
)
(
λ x4 .
co
(
cfv
(
cv
x4
)
(
cv
x1
)
)
(
cfv
(
co
(
co
ci
(
co
c2
cpi
cmul
)
cmul
)
(
co
(
cv
x4
)
(
cv
x3
)
cmul
)
cmul
)
ce
)
cmul
)
)
)
)
⟶
wral
(
λ x1 .
wbr
(
co
(
cdc
c1
cc0
)
(
cdc
c2
c7
)
cexp
)
(
cv
x1
)
cle
⟶
wrex
(
λ x2 .
wrex
(
λ x3 .
w3a
(
wral
(
λ x4 .
wbr
(
cfv
(
cv
x4
)
(
cv
x3
)
)
(
co
c1
(
cdp2
cc0
(
cdp2
c7
(
cdp2
c9
(
cdp2
c9
(
cdp2
c5
c5
)
)
)
)
)
cdp
)
cle
)
(
λ x4 .
cn
)
)
(
wral
(
λ x4 .
wbr
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
co
c1
(
cdp2
c4
(
cdp2
c1
c4
)
)
cdp
)
cle
)
(
λ x4 .
cn
)
)
(
wbr
(
co
(
co
cc0
(
cdp2
cc0
(
cdp2
cc0
(
cdp2
cc0
(
cdp2
c4
(
cdp2
c2
(
cdp2
c2
(
cdp2
c4
c8
)
)
)
)
)
)
)
cdp
)
(
co
(
cv
x1
)
c2
cexp
)
cmul
)
(
citg
(
λ x4 .
co
cc0
c1
cioo
)
(
λ x4 .
co
(
co
(
cfv
(
cv
x4
)
(
co
(
co
cvma
(
cv
x2
)
(
cof
cmul
)
)
(
cv
x1
)
cvts
)
)
(
co
(
cfv
(
cv
x4
)
(
co
(
co
cvma
(
cv
x3
)
(
cof
cmul
)
)
(
cv
x1
)
cvts
)
)
c2
cexp
)
cmul
)
(
cfv
(
co
(
co
ci
(
co
c2
cpi
cmul
)
cmul
)
(
co
(
cneg
(
cv
x1
)
)
(
cv
x4
)
cmul
)
cmul
)
ce
)
cmul
)
)
cle
)
)
(
λ x3 .
co
(
co
cc0
cpnf
cico
)
cn
cmap
)
)
(
λ x2 .
co
(
co
cc0
cpnf
cico
)
cn
cmap
)
)
(
λ x1 .
crab
(
λ x2 .
wn
(
wbr
c2
(
cv
x2
)
cdvds
)
)
(
λ x2 .
cz
)
)
⟶
wral
(
λ x1 .
wbr
(
cfv
(
cv
x1
)
cchp
)
(
co
(
co
c1
(
cdp2
cc0
(
cdp2
c3
(
cdp2
c8
(
cdp2
c8
c3
)
)
)
)
cdp
)
(
cv
x1
)
cmul
)
clt
)
(
λ x1 .
crp
)
⟶
wral
(
λ x1 .
wbr
(
co
(
cfv
(
cv
x1
)
cchp
)
(
cfv
(
cv
x1
)
ccht
)
cmin
)
(
co
(
co
c1
(
cdp2
c4
(
cdp2
c2
(
cdp2
c6
c2
)
)
)
cdp
)
(
cfv
(
cv
x1
)
csqrt
)
cmul
)
clt
)
(
λ x1 .
crp
)
⟶
wceq
cstrkg2d
(
cab
(
λ x1 .
wsbc
(
λ x2 .
wsbc
(
λ x3 .
wsbc
(
λ x4 .
wa
(
wrex
(
λ x5 .
wrex
(
λ x6 .
wrex
(
λ x7 .
wn
(
w3o
(
wcel
(
cv
x7
)
(
co
(
cv
x5
)
(
cv
x6
)
(
cv
x4
)
)
)
(
wcel
(
cv
x5
)
(
co
(
cv
x7
)
(
cv
x6
)
(
cv
x4
)
)
)
(
wcel
(
cv
x6
)
(
co
(
cv
x5
)
(
cv
x7
)
(
cv
x4
)
)
)
)
)
(
λ x7 .
cv
x2
)
)
(
λ x6 .
cv
x2
)
)
(
λ x5 .
cv
x2
)
)
(
wral
(
λ x5 .
wral
(
λ x6 .
wral
(
λ x7 .
wral
(
λ x8 .
wral
(
λ x9 .
wa
(
w3a
(
wceq
(
co
(
cv
x5
)
(
cv
x8
)
(
cv
x3
)
)
(
co
(
cv
x5
)
(
cv
x9
)
(
cv
x3
)
)
)
(
wceq
(
co
(
cv
x6
)
(
cv
x8
)
(
cv
x3
)
)
(
co
(
cv
x6
)
(
cv
x9
)
(
cv
x3
)
)
)
(
wceq
(
co
(
cv
x7
)
(
cv
x8
)
(
cv
x3
)
)
(
co
(
cv
x7
)
(
cv
x9
)
(
cv
x3
)
)
)
)
(
wne
(
cv
x8
)
(
cv
x9
)
)
⟶
w3o
(
wcel
(
cv
x7
)
(
co
(
cv
x5
)
(
cv
x6
)
(
cv
x4
)
)
)
(
wcel
(
cv
x5
)
(
co
(
cv
x7
)
(
cv
x6
)
(
cv
x4
)
)
)
(
wcel
(
cv
x6
)
(
co
(
cv
x5
)
(
cv
x7
)
(
cv
x4
)
)
)
)
(
λ x9 .
cv
x2
)
)
(
λ x8 .
cv
x2
)
)
(
λ x7 .
cv
x2
)
)
(
λ x6 .
cv
x2
)
)
(
λ x5 .
cv
x2
)
)
)
(
cfv
(
cv
x1
)
citv
)
)
(
cfv
(
cv
x1
)
cds
)
)
(
cfv
(
cv
x1
)
cbs
)
)
)
⟶
wceq
cafs
(
cmpt
(
λ x1 .
cstrkg
)
(
λ x1 .
copab
(
λ x2 x3 .
wsbc
(
λ x4 .
wsbc
(
λ x5 .
wsbc
(
λ x6 .
wrex
(
λ x7 .
wrex
(
λ x8 .
wrex
(
λ x9 .
wrex
(
λ x10 .
wrex
(
λ x11 .
wrex
(
λ x12 .
wrex
(
λ x13 .
wrex
(
λ x14 .
w3a
(
wceq
(
cv
x2
)
(
cop
(
cop
(
cv
x7
)
(
cv
x8
)
)
(
cop
(
cv
x9
)
(
cv
x10
)
)
)
)
(
wceq
(
cv
x3
)
(
cop
(
cop
(
cv
x11
)
(
cv
x12
)
)
(
cop
(
cv
x13
)
(
cv
x14
)
)
)
)
(
w3a
(
wa
(
wcel
(
cv
x8
)
(
co
(
cv
x7
)
(
cv
x9
)
(
cv
x6
)
)
)
(
wcel
(
cv
x12
)
(
co
(
cv
x11
)
(
cv
x13
)
(
cv
x6
)
)
)
)
(
wa
(
wceq
(
co
(
cv
x7
)
(
cv
x8
)
(
cv
x5
)
)
(
co
(
cv
x11
)
(
cv
x12
)
(
cv
x5
)
)
)
(
wceq
(
co
(
cv
x8
)
(
cv
x9
)
(
cv
x5
)
)
(
co
(
cv
x12
)
(
cv
x13
)
(
cv
x5
)
)
)
)
(
wa
(
wceq
(
co
(
cv
x7
)
(
cv
x10
)
(
cv
x5
)
)
(
co
(
cv
x11
)
(
cv
x14
)
(
cv
x5
)
)
)
(
wceq
(
co
(
cv
x8
)
(
cv
x10
)
(
cv
x5
)
)
(
co
(
cv
x12
)
(
cv
x14
)
(
cv
x5
)
)
)
)
)
)
(
λ x14 .
cv
x4
)
)
(
λ x13 .
cv
x4
)
)
(
λ x12 .
cv
x4
)
)
(
λ x11 .
cv
x4
)
)
(
λ x10 .
cv
x4
)
)
(
λ x9 .
cv
x4
)
)
(
λ x8 .
cv
x4
)
)
(
λ x7 .
cv
x4
)
)
(
cfv
(
cv
x1
)
citv
)
)
(
cfv
(
cv
x1
)
cds
)
)
(
cfv
(
cv
x1
)
cbs
)
)
)
)
⟶
(
∀ x1 x2 x3 x4 : ο .
wb
(
w_bnj17
x1
x2
x3
x4
)
(
wa
(
w3a
x1
x2
x3
)
x4
)
)
⟶
(
∀ x1 x2 x3 :
ι → ο
.
wceq
(
c_bnj14
x1
x2
x3
)
(
crab
(
λ x4 .
wbr
(
cv
x4
)
x3
x2
)
(
λ x4 .
x1
)
)
)
⟶
(
∀ x1 x2 :
ι → ο
.
wb
(
w_bnj13
x1
x2
)
(
wral
(
λ x3 .
wcel
(
c_bnj14
x1
x2
(
cv
x3
)
)
cvv
)
(
λ x3 .
x1
)
)
)
⟶
(
∀ x1 x2 :
ι → ο
.
wb
(
w_bnj15
x1
x2
)
(
wa
(
wfr
x1
x2
)
(
w_bnj13
x1
x2
)
)
)
⟶
(
∀ x1 x2 x3 :
ι → ο
.
wceq
(
c_bnj18
x1
x2
x3
)
(
ciun
(
λ x4 .
cab
(
λ x5 .
wrex
(
λ x6 .
w3a
(
wfn
(
cv
x5
)
(
cv
x6
)
)
(
wceq
(
cfv
c0
(
cv
x5
)
)
(
c_bnj14
x1
x2
x3
)
)
(
wral
(
λ x7 .
wcel
(
csuc
(
cv
x7
)
)
(
cv
x6
)
⟶
wceq
(
cfv
(
csuc
(
cv
x7
)
)
(
cv
x5
)
)
(
ciun
(
λ x8 .
cfv
(
cv
x7
)
(
cv
x5
)
)
(
λ x8 .
c_bnj14
x1
x2
(
cv
x8
)
)
)
)
(
λ x7 .
com
)
)
)
(
λ x6 .
cdif
com
(
csn
c0
)
)
)
)
(
λ x4 .
ciun
(
λ x5 .
cdm
(
cv
x4
)
)
(
λ x5 .
cfv
(
cv
x5
)
(
cv
x4
)
)
)
)
)
⟶
(
∀ x1 x2 x3 :
ι → ο
.
wb
(
w_bnj19
x1
x2
x3
)
(
wral
(
λ x4 .
wss
(
c_bnj14
x1
x3
(
cv
x4
)
)
x2
)
(
λ x4 .
x2
)
)
)
⟶
(
∀ x1 :
ι →
ι → ο
.
(
∀ x2 x3 .
x1
x2
x3
)
⟶
∀ x2 x3 .
x1
x3
x2
)
⟶
(
∀ x1 x2 x3 .
wceq
(
cv
x1
)
(
cv
x2
)
⟶
wceq
(
cv
x1
)
(
cv
x3
)
⟶
wceq
(
cv
x2
)
(
cv
x3
)
)
⟶
wn
(
∀ x1 .
wn
(
wceq
(
cv
x1
)
(
cv
x1
)
)
)
⟶
(
∀ x1 .
wn
(
∀ x2 .
wn
(
wceq
(
cv
x2
)
(
cv
x1
)
)
)
)
⟶
(
∀ x1 x2 .
(
∀ x3 .
wceq
(
cv
x3
)
(
cv
x2
)
)
⟶
∀ x3 .
wceq
(
cv
x3
)
(
cv
x1
)
)
⟶
(
∀ x1 :
ι →
ι → ο
.
∀ x2 x3 .
wceq
(
cv
x2
)
(
cv
x3
)
⟶
(
∀ x4 .
x1
x2
x4
)
⟶
∀ x4 .
wceq
(
cv
x4
)
(
cv
x3
)
⟶
x1
x4
x3
)
⟶
x0
)
⟶
x0
type
prop
theory
SetMM
name
df_vts__ax_hgt749__ax_ros335__ax_ros336__df_trkg2d__df_afs__df_bnj17__df_bnj14__df_bnj13__df_bnj15__df_bnj18__df_bnj19__ax_7d__ax_8d__ax_9d1__ax_9d2__ax_10d__ax_11d
proof
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