Search for blocks/addresses/...
Proofgold Proof
pf
Apply df_cart__df_img__df_domain__df_range__df_cup__df_cap__df_restrict__df_succf__df_apply__df_funpart__df_fullfun__df_ub__df_lb__df_altop__df_altxp__df_ofs__df_transport__df_colinear with
wceq
ctransport
(
coprab
(
λ x0 x1 x2 .
wrex
(
λ x3 .
wa
(
w3a
(
wcel
(
cv
x0
)
(
cxp
(
cfv
(
cv
x3
)
cee
)
(
cfv
(
cv
x3
)
cee
)
)
)
(
wcel
(
cv
x1
)
(
cxp
(
cfv
(
cv
x3
)
cee
)
(
cfv
(
cv
x3
)
cee
)
)
)
(
wne
(
cfv
(
cv
x1
)
c1st
)
(
cfv
(
cv
x1
)
c2nd
)
)
)
(
wceq
(
cv
x2
)
(
crio
(
λ x4 .
wa
(
wbr
(
cfv
(
cv
x1
)
c2nd
)
(
cop
(
cfv
(
cv
x1
)
c1st
)
(
cv
x4
)
)
cbtwn
)
(
wbr
(
cop
(
cfv
(
cv
x1
)
c2nd
)
(
cv
x4
)
)
(
cv
x0
)
ccgr
)
)
(
λ x4 .
cfv
(
cv
x3
)
cee
)
)
)
)
(
λ x3 .
cn
)
)
)
.
Assume H0:
wceq
ccart
(
cdif
(
cxp
(
cxp
cvv
cvv
)
cvv
)
(
crn
(
csymdif
(
ctxp
cvv
cep
)
(
ctxp
(
cpprod
cep
cep
)
cvv
)
)
)
)
.
Assume H1:
wceq
cimg
(
ccom
(
cimage
(
cres
(
ccom
c2nd
c1st
)
(
cres
c1st
(
cxp
cvv
cvv
)
)
)
)
ccart
)
.
Assume H2:
wceq
cdomain
(
cimage
(
cres
c1st
(
cxp
cvv
cvv
)
)
)
.
Assume H3:
wceq
crange
(
cimage
(
cres
c2nd
(
cxp
cvv
cvv
)
)
)
.
Assume H4:
wceq
ccup
(
cdif
(
cxp
(
cxp
cvv
cvv
)
cvv
)
(
crn
(
csymdif
(
ctxp
cvv
cep
)
(
ctxp
(
cun
(
ccom
(
ccnv
c1st
)
cep
)
(
ccom
(
ccnv
c2nd
)
cep
)
)
cvv
)
)
)
)
.
Assume H5:
wceq
ccap
(
cdif
(
cxp
(
cxp
cvv
cvv
)
cvv
)
(
crn
(
csymdif
(
ctxp
cvv
cep
)
(
ctxp
(
cin
(
ccom
(
ccnv
c1st
)
cep
)
(
ccom
(
ccnv
c2nd
)
cep
)
)
cvv
)
)
)
)
.
Assume H6:
wceq
crestrict
(
ccom
ccap
(
ctxp
c1st
(
ccom
ccart
(
ctxp
c2nd
(
ccom
crange
c1st
)
)
)
)
)
.
Assume H7:
wceq
csuccf
(
ccom
ccup
(
ctxp
cid
csingle
)
)
.
Assume H8:
wceq
capply
(
ccom
(
ccom
cbigcup
cbigcup
)
(
ccom
(
cdif
(
cxp
cvv
cvv
)
(
crn
(
csymdif
(
ctxp
cvv
cep
)
(
ctxp
(
cres
cep
csingles
)
cvv
)
)
)
)
(
ccom
(
ccom
csingle
cimg
)
(
cpprod
cid
csingle
)
)
)
)
.
Assume H9:
∀ x0 :
ι → ο
.
wceq
(
cfunpart
x0
)
(
cres
x0
(
cdm
(
cin
(
ccom
(
cimage
x0
)
csingle
)
(
cxp
cvv
csingles
)
)
)
)
.
Assume H10:
∀ x0 :
ι → ο
.
wceq
(
cfullfn
x0
)
(
cun
(
cfunpart
x0
)
(
cxp
...
...
)
)
.
...
■