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Proofgold Proof
pf
Apply andI with
0
∈
omega
,
∃ x0 .
and
(
x0
∈
omega
)
(
0
=
mul_nat
2
x0
)
leaving 2 subgoals.
Apply nat_p_omega with
0
.
The subproof is completed by applying nat_0.
Let x0 of type
ο
be given.
Assume H0:
∀ x1 .
and
(
x1
∈
omega
)
(
0
=
mul_nat
2
x1
)
⟶
x0
.
Apply H0 with
0
.
Apply andI with
0
∈
omega
,
0
=
mul_nat
2
0
leaving 2 subgoals.
Apply nat_p_omega with
0
.
The subproof is completed by applying nat_0.
Let x1 of type
ι
→
ι
→
ο
be given.
The subproof is completed by applying mul_nat_0R with
2
,
λ x2 x3 .
x1
x3
x2
.
■