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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
RealsStruct
x0
.
Apply H0 with
∀ x1 .
x1
∈
field0
x0
⟶
∀ x2 .
x2
∈
field0
x0
⟶
field1b
x0
x1
x2
∈
field0
x0
.
Apply RealsStruct_eta with
x0
,
λ x1 x2 .
struct_b_b_r_e_e
x2
⟶
unpack_b_b_r_e_e_o
x0
(
λ x3 .
λ x4 x5 :
ι →
ι → ι
.
λ x6 :
ι →
ι → ο
.
λ x7 x8 .
explicit_Reals
x3
x7
x8
x4
x5
x6
)
⟶
∀ x3 .
x3
∈
field0
x0
⟶
∀ x4 .
x4
∈
field0
x0
⟶
field1b
x0
x3
x4
∈
field0
x0
leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1:
struct_b_b_r_e_e
(
pack_b_b_r_e_e
(
field0
x0
)
(
field1b
x0
)
(
field2b
x0
)
(
RealsStruct_leq
x0
)
(
field4
x0
)
(
RealsStruct_one
x0
)
)
.
Assume H2:
unpack_b_b_r_e_e_o
x0
(
λ x1 .
λ x2 x3 :
ι →
ι → ι
.
λ x4 :
ι →
ι → ο
.
λ x5 x6 .
explicit_Reals
x1
x5
x6
x2
x3
x4
)
.
Apply pack_struct_b_b_r_e_e_E1 with
field0
x0
,
field1b
x0
,
field2b
x0
,
RealsStruct_leq
x0
,
field4
x0
,
RealsStruct_one
x0
.
The subproof is completed by applying H1.
■