Search for blocks/addresses/...
Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Assume H0:
∀ x2 .
x2
∈
SNoS_
omega
⟶
(
∀ x3 .
x3
∈
omega
⟶
SNoLt
(
abs_SNo
(
add_SNo
x2
(
minus_SNo
x0
)
)
)
(
eps_
x3
)
)
⟶
x2
=
x0
.
Assume H1:
SNo
x1
.
Assume H2:
SNoLt
x0
x1
.
Assume H3:
x1
∈
SNoS_
omega
.
Assume H4:
SNoLt
0
(
add_SNo
x1
(
minus_SNo
x0
)
)
.
Assume H5:
not
(
∃ x2 .
and
(
x2
∈
omega
)
(
SNoLe
(
add_SNo
x0
(
eps_
x2
)
)
x1
)
)
.
Assume H6:
x1
=
x0
.
Apply SNoLt_irref with
x1
.
Apply H6 with
λ x2 x3 .
SNoLt
x3
x1
.
The subproof is completed by applying H2.
■