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Definition
ccnp
:=
ccnp
Definition
cmpt2
:=
cmpt2
Definition
cima
:=
cima
Definition
clm
:=
clm
Definition
cc
:=
cc
Definition
cpm
:=
cpm
Definition
wf
:=
wf
Definition
cres
:=
cres
Definition
cuz
:=
cuz
Definition
ct0
:=
ct0
Definition
wb
:=
wb
Definition
ct1
:=
ct1
Definition
cha
:=
cha
Definition
w3a
:=
w3a
Definition
creg
:=
creg
Definition
ccl
:=
ccl
Definition
ccnrm
:=
ccnrm
Definition
cpnrm
:=
cpnrm
Definition
cn
:=
cn
Definition
cmap
:=
cmap
Definition
cint
:=
cint
Definition
crn
:=
crn
Definition
cnrm
:=
cnrm
Definition
ccmp
:=
ccmp
Definition
cconn
:=
cconn
Definition
ccld
:=
ccld
Definition
cpr
:=
cpr
Definition
c1stc
:=
c1stc
Definition
c2ndc
:=
c2ndc
Definition
wbr
:=
wbr
Definition
com
:=
com
Definition
cdom
:=
cdom
Definition
ctg
:=
ctg
Definition
ctb
:=
ctb
Definition
clly
:=
clly
Definition
cnlly
:=
cnlly
Definition
co
:=
co
Definition
crest
:=
crest
Definition
csn
:=
csn
Definition
cfv
:=
cfv
Definition
cnei
:=
cnei
Definition
cpw
:=
cpw
Definition
cref
:=
cref
Definition
copab
:=
copab
Definition
wss
:=
wss
Definition
cptfin
:=
cptfin
Definition
clocfin
:=
clocfin
Definition
cmpt
:=
cmpt
Definition
ctop
:=
ctop
Definition
cab
:=
cab
Definition
wceq
wceq
:=
wceq
Definition
wral
:=
wral
Definition
wrex
:=
wrex
Definition
wa
:=
wa
Definition
wcel
:=
wcel
Definition
crab
:=
crab
Definition
wne
:=
wne
Definition
cin
:=
cin
Definition
c0
:=
c0
Definition
cfn
:=
cfn
Definition
cuni
:=
cuni
Definition
cv
:=
cv
Known
df_cnp__df_lm__df_t0__df_t1__df_haus__df_reg__df_nrm__df_cnrm__df_pnrm__df_cmp__df_conn__df_1stc__df_2ndc__df_lly__df_nlly__df_ref__df_ptfin__df_locfin
:
∀ x0 : ο .
(
wceq
ccnp
(
cmpt2
(
λ x1 x2 .
ctop
)
(
λ x1 x2 .
ctop
)
(
λ x1 x2 .
cmpt
(
λ x3 .
cuni
(
cv
x1
)
)
(
λ x3 .
crab
(
λ x4 .
wral
(
λ x5 .
wcel
(
cfv
(
cv
x3
)
(
cv
x4
)
)
(
cv
x5
)
⟶
wrex
(
λ x6 .
wa
(
wcel
(
cv
x3
)
(
cv
x6
)
)
(
wss
(
cima
(
cv
x4
)
(
cv
x6
)
)
(
cv
x5
)
)
)
(
λ x6 .
cv
x1
)
)
(
λ x5 .
cv
x2
)
)
(
λ x4 .
co
(
cuni
(
cv
x2
)
)
(
cuni
(
cv
x1
)
)
cmap
)
)
)
)
⟶
wceq
clm
(
cmpt
(
λ x1 .
ctop
)
(
λ x1 .
copab
(
λ x2 x3 .
w3a
(
wcel
(
cv
x2
)
(
co
(
cuni
(
cv
x1
)
)
cc
cpm
)
)
(
wcel
(
cv
x3
)
(
cuni
(
cv
x1
)
)
)
(
wral
(
λ x4 .
wcel
(
cv
x3
)
(
cv
x4
)
⟶
wrex
(
λ x5 .
wf
(
cv
x5
)
(
cv
x4
)
(
cres
(
cv
x2
)
(
cv
x5
)
)
)
(
λ x5 .
crn
cuz
)
)
(
λ x4 .
cv
x1
)
)
)
)
)
⟶
wceq
ct0
(
crab
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wb
(
wcel
(
cv
x2
)
(
cv
x4
)
)
(
wcel
(
cv
x3
)
(
cv
x4
)
)
)
(
λ x4 .
cv
x1
)
⟶
wceq
(
cv
x2
)
(
cv
x3
)
)
(
λ x3 .
cuni
(
cv
x1
)
)
)
(
λ x2 .
cuni
(
cv
x1
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
ct1
(
crab
(
λ x1 .
wral
(
λ x2 .
wcel
(
csn
(
cv
x2
)
)
(
cfv
(
cv
x1
)
ccld
)
)
(
λ x2 .
cuni
(
cv
x1
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
cha
(
crab
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wne
(
cv
x2
)
(
cv
x3
)
⟶
wrex
(
λ x4 .
wrex
(
λ x5 .
w3a
(
wcel
(
cv
x2
)
(
cv
x4
)
)
(
wcel
(
cv
x3
)
(
cv
x5
)
)
(
wceq
(
cin
(
cv
x4
)
(
cv
x5
)
)
c0
)
)
(
λ x5 .
cv
x1
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cuni
(
cv
x1
)
)
)
(
λ x2 .
cuni
(
cv
x1
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
creg
(
crab
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wrex
(
λ x4 .
wa
(
wcel
(
cv
x3
)
(
cv
x4
)
)
(
wss
(
cfv
(
cv
x4
)
(
cfv
(
cv
x1
)
ccl
)
)
(
cv
x2
)
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cv
x2
)
)
(
λ x2 .
cv
x1
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
cnrm
(
crab
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wrex
(
λ x4 .
wa
(
wss
(
cv
x3
)
(
cv
x4
)
)
(
wss
(
cfv
(
cv
x4
)
(
cfv
(
cv
x1
)
ccl
)
)
(
cv
x2
)
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cin
(
cfv
(
cv
x1
)
ccld
)
(
cpw
(
cv
x2
)
)
)
)
(
λ x2 .
cv
x1
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
ccnrm
(
crab
(
λ x1 .
wral
(
λ x2 .
wcel
(
co
(
cv
x1
)
(
cv
x2
)
crest
)
cnrm
)
(
λ x2 .
cpw
(
cuni
(
cv
x1
)
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
cpnrm
(
crab
(
λ x1 .
wss
(
cfv
(
cv
x1
)
ccld
)
(
crn
(
cmpt
(
λ x2 .
co
(
cv
x1
)
cn
cmap
)
(
λ x2 .
cint
(
crn
(
cv
x2
)
)
)
)
)
)
(
λ x1 .
cnrm
)
)
⟶
wceq
ccmp
(
crab
(
λ x1 .
wral
(
λ x2 .
wceq
(
cuni
(
cv
x1
)
)
(
cuni
(
cv
x2
)
)
⟶
wrex
(
λ x3 .
wceq
(
cuni
(
cv
x1
)
)
(
cuni
(
cv
x3
)
)
)
(
λ x3 .
cin
(
cpw
(
cv
x2
)
)
cfn
)
)
(
λ x2 .
cpw
(
cv
x1
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
cconn
(
crab
(
λ x1 .
wceq
(
cin
(
cv
x1
)
(
cfv
(
cv
x1
)
ccld
)
)
(
cpr
c0
(
cuni
(
cv
x1
)
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
c1stc
(
crab
(
λ x1 .
wral
(
λ x2 .
wrex
(
λ x3 .
wa
(
wbr
(
cv
x3
)
com
cdom
)
(
wral
(
λ x4 .
wcel
(
cv
x2
)
(
cv
x4
)
⟶
wcel
(
cv
x2
)
(
cuni
(
cin
(
cv
x3
)
(
cpw
(
cv
x4
)
)
)
)
)
(
λ x4 .
cv
x1
)
)
)
(
λ x3 .
cpw
(
cv
x1
)
)
)
(
λ x2 .
cuni
(
cv
x1
)
)
)
(
λ x1 .
ctop
)
)
⟶
wceq
c2ndc
(
cab
(
λ x1 .
wrex
(
λ x2 .
wa
(
wbr
(
cv
x2
)
com
cdom
)
(
wceq
(
cfv
(
cv
x2
)
ctg
)
(
cv
x1
)
)
)
(
λ x2 .
ctb
)
)
)
⟶
(
∀ x1 :
ι → ο
.
wceq
(
clly
x1
)
(
crab
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wrex
(
λ x5 .
wa
(
wcel
(
cv
x4
)
(
cv
x5
)
)
(
wcel
(
co
(
cv
x2
)
(
cv
x5
)
crest
)
x1
)
)
(
λ x5 .
cin
(
cv
x2
)
(
cpw
(
cv
x3
)
)
)
)
(
λ x4 .
cv
x3
)
)
(
λ x3 .
cv
x2
)
)
(
λ x2 .
ctop
)
)
)
⟶
(
∀ x1 :
ι → ο
.
wceq
(
cnlly
x1
)
(
crab
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wrex
(
λ x5 .
wcel
(
co
(
cv
x2
)
(
cv
x5
)
crest
)
x1
)
(
λ x5 .
cin
(
cfv
(
csn
(
cv
x4
)
)
(
cfv
(
cv
x2
)
cnei
)
)
(
cpw
(
cv
x3
)
)
)
)
(
λ x4 .
cv
x3
)
)
(
λ x3 .
cv
x2
)
)
(
λ x2 .
ctop
)
)
)
⟶
wceq
cref
(
copab
(
λ x1 x2 .
wa
(
wceq
(
cuni
(
cv
x2
)
)
(
cuni
(
cv
x1
)
)
)
(
wral
(
λ x3 .
wrex
(
λ x4 .
wss
(
cv
x3
)
(
cv
x4
)
)
(
λ x4 .
cv
x2
)
)
(
λ x3 .
cv
x1
)
)
)
)
⟶
wceq
cptfin
(
cab
(
λ x1 .
wral
(
λ x2 .
wcel
(
crab
(
λ x3 .
wcel
(
cv
x2
)
(
cv
x3
)
)
(
λ x3 .
cv
x1
)
)
cfn
)
(
λ x2 .
cuni
(
cv
x1
)
)
)
)
⟶
wceq
clocfin
(
cmpt
(
λ x1 .
ctop
)
(
λ x1 .
cab
(
λ x2 .
wa
(
wceq
(
cuni
(
cv
x1
)
)
(
cuni
(
cv
x2
)
)
)
(
wral
(
λ x3 .
wrex
(
λ x4 .
wa
(
wcel
(
cv
x3
)
(
cv
x4
)
)
(
wcel
(
crab
(
λ x5 .
wne
(
cin
(
cv
x5
)
(
cv
x4
)
)
c0
)
(
λ x5 .
cv
x2
)
)
cfn
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
cuni
(
cv
x1
)
)
)
)
)
)
⟶
x0
)
⟶
x0
Theorem
df_cnp
:
wceq
ccnp
(
cmpt2
(
λ x0 x1 .
ctop
)
(
λ x0 x1 .
ctop
)
(
λ x0 x1 .
cmpt
(
λ x2 .
cuni
(
cv
x0
)
)
(
λ x2 .
crab
(
λ x3 .
wral
(
λ x4 .
wcel
(
cfv
(
cv
x2
)
(
cv
x3
)
)
(
cv
x4
)
⟶
wrex
(
λ x5 .
wa
(
wcel
(
cv
x2
)
(
cv
x5
)
)
(
wss
(
cima
(
cv
x3
)
(
cv
x5
)
)
(
cv
x4
)
)
)
(
λ x5 .
cv
x0
)
)
(
λ x4 .
cv
x1
)
)
(
λ x3 .
co
(
cuni
(
cv
x1
)
)
(
cuni
(
cv
x0
)
)
cmap
)
)
)
)
(proof)
Theorem
df_t0
:
wceq
ct0
(
crab
(
λ x0 .
wral
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wb
(
wcel
(
cv
x1
)
(
cv
x3
)
)
(
wcel
(
cv
x2
)
(
cv
x3
)
)
)
(
λ x3 .
cv
x0
)
⟶
wceq
(
cv
x1
)
(
cv
x2
)
)
(
λ x2 .
cuni
(
cv
x0
)
)
)
(
λ x1 .
cuni
(
cv
x0
)
)
)
(
λ x0 .
ctop
)
)
(proof)
Theorem
df_haus
:
wceq
cha
(
crab
(
λ x0 .
wral
(
λ x1 .
wral
(
λ x2 .
wne
(
cv
x1
)
(
cv
x2
)
⟶
wrex
(
λ x3 .
wrex
(
λ x4 .
w3a
(
wcel
(
cv
x1
)
(
cv
x3
)
)
(
wcel
(
cv
x2
)
(
cv
x4
)
)
(
wceq
(
cin
(
cv
x3
)
(
cv
x4
)
)
c0
)
)
(
λ x4 .
cv
x0
)
)
(
λ x3 .
cv
x0
)
)
(
λ x2 .
cuni
(
cv
x0
)
)
)
(
λ x1 .
cuni
(
cv
x0
)
)
)
(
λ x0 .
ctop
)
)
(proof)
Theorem
df_nrm
:
wceq
cnrm
(
crab
(
λ x0 .
wral
(
λ x1 .
wral
(
λ x2 .
wrex
(
λ x3 .
wa
(
wss
(
cv
x2
)
(
cv
x3
)
)
(
wss
(
cfv
(
cv
x3
)
(
cfv
(
cv
x0
)
ccl
)
)
(
cv
x1
)
)
)
(
λ x3 .
cv
x0
)
)
(
λ x2 .
cin
(
cfv
(
cv
x0
)
ccld
)
(
cpw
(
cv
x1
)
)
)
)
(
λ x1 .
cv
x0
)
)
(
λ x0 .
ctop
)
)
(proof)
Theorem
df_pnrm
:
wceq
cpnrm
(
crab
(
λ x0 .
wss
(
cfv
(
cv
x0
)
ccld
)
(
crn
(
cmpt
(
λ x1 .
co
(
cv
x0
)
cn
cmap
)
(
λ x1 .
cint
(
crn
(
cv
x1
)
)
)
)
)
)
(
λ x0 .
cnrm
)
)
(proof)
Theorem
df_conn
:
wceq
cconn
(
crab
(
λ x0 .
wceq
(
cin
(
cv
x0
)
(
cfv
(
cv
x0
)
ccld
)
)
(
cpr
c0
(
cuni
(
cv
x0
)
)
)
)
(
λ x0 .
ctop
)
)
(proof)
Theorem
df_2ndc
:
wceq
c2ndc
(
cab
(
λ x0 .
wrex
(
λ x1 .
wa
(
wbr
(
cv
x1
)
com
cdom
)
(
wceq
(
cfv
(
cv
x1
)
ctg
)
(
cv
x0
)
)
)
(
λ x1 .
ctb
)
)
)
(proof)
Theorem
df_nlly
:
∀ x0 :
ι → ο
.
wceq
(
cnlly
x0
)
(
crab
(
λ x1 .
wral
(
λ x2 .
wral
(
λ x3 .
wrex
(
λ x4 .
wcel
(
co
(
cv
x1
)
(
cv
x4
)
crest
)
x0
)
(
λ x4 .
cin
(
cfv
(
csn
(
cv
x3
)
)
(
cfv
(
cv
x1
)
cnei
)
)
(
cpw
(
cv
x2
)
)
)
)
(
λ x3 .
cv
x2
)
)
(
λ x2 .
cv
x1
)
)
(
λ x1 .
ctop
)
)
(proof)
Theorem
df_ptfin
:
wceq
cptfin
(
cab
(
λ x0 .
wral
(
λ x1 .
wcel
(
crab
(
λ x2 .
wcel
(
cv
x1
)
(
cv
x2
)
)
(
λ x2 .
cv
x0
)
)
cfn
)
(
λ x1 .
cuni
(
cv
x0
)
)
)
)
(proof)
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