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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
Field
x0
.
Apply H0 with
explicit_Field
(
field0
x0
)
(
field3
x0
)
(
field4
x0
)
(
field1b
x0
)
(
field2b
x0
)
.
Assume H1:
struct_b_b_e_e
x0
.
Apply Field_eta with
x0
,
λ x1 x2 .
unpack_b_b_e_e_o
x2
(
λ x3 .
λ x4 x5 :
ι →
ι → ι
.
λ x6 x7 .
explicit_Field
x3
x6
x7
x4
x5
)
⟶
explicit_Field
(
field0
x0
)
(
field3
x0
)
(
field4
x0
)
(
field1b
x0
)
(
field2b
x0
)
leaving 2 subgoals.
The subproof is completed by applying H0.
Apply Field_unpack_eq with
field0
x0
,
field1b
x0
,
field2b
x0
,
field3
x0
,
field4
x0
,
λ x1 x2 : ο .
x2
⟶
explicit_Field
(
field0
x0
)
(
field3
x0
)
(
field4
x0
)
(
field1b
x0
)
(
field2b
x0
)
.
Assume H2:
explicit_Field
(
field0
x0
)
(
field3
x0
)
(
field4
x0
)
(
field1b
x0
)
(
field2b
x0
)
.
The subproof is completed by applying H2.
■