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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
→
ι
→
ι
be given.
Assume H0:
abelian_Group
(
pack_b
x0
x1
)
.
Apply H0 with
and
(
Group
(
pack_b
x0
x1
)
)
(
explicit_abelian
x0
x1
)
.
Assume H1:
Group
(
pack_b
x0
x1
)
.
Apply abelian_Group_unpack_eq with
x0
,
x1
,
λ x2 x3 : ο .
x3
⟶
and
(
Group
(
pack_b
x0
x1
)
)
(
explicit_abelian
x0
x1
)
.
Assume H2:
explicit_abelian
x0
x1
.
Apply andI with
Group
(
pack_b
x0
x1
)
,
explicit_abelian
x0
x1
leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
■