Search for blocks/addresses/...
Proofgold Proof
pf
Apply df_gbow__df_gbo__ax_bgbltosilva__ax_tgoldbachgt__ax_hgprmladder__ax_bgbltosilvaOLD__ax_hgprmladderOLD__ax_tgoldbachgtOLD__df_upwlks__df_spr__df_mgmhm__df_submgm__df_cllaw__df_comlaw__df_asslaw__df_intop__df_clintop__df_assintop with
wceq
cmgmhm
(
cmpt2
(
λ x0 x1 .
cmgm
)
(
λ x0 x1 .
cmgm
)
(
λ x0 x1 .
crab
(
λ x2 .
wral
(
λ x3 .
wral
(
λ x4 .
wceq
(
cfv
(
co
(
cv
x3
)
(
cv
x4
)
(
cfv
(
cv
x0
)
cplusg
)
)
(
cv
x2
)
)
(
co
(
cfv
(
cv
x3
)
(
cv
x2
)
)
(
cfv
(
cv
x4
)
(
cv
x2
)
)
(
cfv
(
cv
x1
)
cplusg
)
)
)
(
λ x4 .
cfv
(
cv
x0
)
cbs
)
)
(
λ x3 .
cfv
(
cv
x0
)
cbs
)
)
(
λ x2 .
co
(
cfv
(
cv
x1
)
cbs
)
(
cfv
(
cv
x0
)
cbs
)
cmap
)
)
)
.
Assume H0:
wceq
cgbow
(
crab
(
λ x0 .
wrex
(
λ x1 .
wrex
(
λ x2 .
wrex
(
λ x3 .
wceq
(
cv
x0
)
(
co
(
co
(
cv
x1
)
(
cv
x2
)
caddc
)
(
cv
x3
)
caddc
)
)
(
λ x3 .
cprime
)
)
(
λ x2 .
cprime
)
)
(
λ x1 .
cprime
)
)
(
λ x0 .
codd
)
)
.
Assume H1:
wceq
cgbo
(
crab
(
λ x0 .
wrex
(
λ x1 .
wrex
(
λ x2 .
wrex
(
λ x3 .
wa
(
w3a
(
wcel
(
cv
x1
)
codd
)
(
wcel
(
cv
x2
)
codd
)
(
wcel
(
cv
x3
)
codd
)
)
(
wceq
(
cv
x0
)
(
co
(
co
(
cv
x1
)
(
cv
x2
)
caddc
)
(
cv
x3
)
caddc
)
)
)
(
λ x3 .
cprime
)
)
(
λ x2 .
cprime
)
)
(
λ x1 .
cprime
)
)
(
λ x0 .
codd
)
)
.
Assume H2:
∀ x0 :
ι → ο
.
w3a
(
wcel
x0
ceven
)
(
wbr
c4
x0
clt
)
(
wbr
x0
(
co
c4
(
co
(
cdc
c1
cc0
)
(
cdc
c1
c8
)
cexp
)
cmul
)
cle
)
⟶
wcel
x0
cgbe
.
Assume H3:
∀ x0 :
ι →
ι →
ι →
ι →
ι →
ι → ο
.
∀ x1 :
ι →
ι → ο
.
...
⟶
(
∀ x2 x3 x4 x5 x6 .
wceq
(
x0
x2
x3
x4
x5
x6
)
(
crab
(
λ x7 .
wrex
(
λ x8 .
wrex
(
λ x9 .
wrex
(
λ x10 .
wa
(
w3a
(
wcel
(
cv
x8
)
(
x1
x3
)
)
(
wcel
(
cv
x9
)
(
x1
x3
)
)
(
wcel
(
cv
x10
)
(
x1
x3
)
)
)
(
wceq
(
cv
x7
)
(
co
(
co
(
cv
x8
)
(
cv
x9
)
caddc
)
(
cv
x10
)
caddc
)
)
)
...
)
...
)
...
)
...
)
)
⟶
∀ x2 x3 x4 x5 .
wrex
(
λ x6 .
wa
(
wbr
(
cv
x6
)
(
co
(
cdc
c1
cc0
)
(
cdc
c2
c7
)
cexp
)
cle
)
(
wral
(
λ x7 .
wbr
(
cv
x6
)
(
cv
x7
)
clt
⟶
wcel
(
cv
x7
)
(
x0
x2
x7
x3
x4
x5
)
)
(
λ x7 .
x1
x7
)
)
)
(
λ x6 .
cn
)
.
...
■