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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
wrex
(
λ x0 .
wrex
(
λ x1 .
wa
(
w3a
(
wceq
(
cfv
cc0
(
cv
x1
)
)
c7
)
(
wceq
(
cfv
c1
(
cv
x1
)
)
(
cdc
c1
c3
)
)
(
wceq
(
cfv
(
cv
x0
)
(
cv
x1
)
)
(
co
(
cdc
c8
c9
)
(
co
(
cdc
c1
cc0
)
(
cdc
c2
c9
)
cexp
)
cmul
)
)
)
(
wral
(
λ x2 .
w3a
(
wcel
(
cfv
(
cv
x2
)
(
cv
x1
)
)
(
cdif
cprime
(
csn
c2
)
)
)
(
wbr
(
co
(
cfv
(
co
(
cv
x2
)
c1
caddc
)
(
cv
x1
)
)
(
cfv
(
cv
x2
)
(
cv
x1
)
)
cmin
)
(
co
(
co
c4
(
co
(
cdc
c1
cc0
)
(
cdc
c1
c8
)
cexp
)
cmul
)
c4
cmin
)
clt
)
(
wbr
c4
(
co
(
cfv
(
co
(
cv
x2
)
c1
caddc
)
(
cv
x1
)
)
(
cfv
(
cv
x2
)
(
cv
x1
)
)
cmin
)
clt
)
)
(
λ x2 .
co
cc0
(
cv
x0
)
cfzo
)
)
)
(
λ x1 .
cfv
(
cv
x0
)
ciccp
)
)
(
λ x0 .
cfv
c3
cuz
)
.
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 .
wrex
(
λ x6 .
wa
(
wbr
(
cv
x6
)
(
co
(
cdc
c1
cc0
)
(
cdc
c2
c7
)
cexp
)
cle
)
(
wral
(
λ x7 .
wbr
(
cv
x6
)
(
cv
...
)
...
⟶
wcel
(
cv
x7
)
(
x0
x2
x7
x3
x4
x5
)
)
...
)
)
...
.
...
■