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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
RealsStruct
x0
.
Apply Field_of_RealsStruct_3 with
x0
,
λ x1 x2 .
∀ x3 .
x3
∈
field0
x0
⟶
field2b
x0
x3
x1
=
x1
.
Apply Field_of_RealsStruct_2f with
x0
,
λ x1 x2 :
ι →
ι → ι
.
∀ x3 .
x3
∈
field0
x0
⟶
x1
x3
(
ap
(
Field_of_RealsStruct
x0
)
3
)
=
ap
(
Field_of_RealsStruct
x0
)
3
leaving 2 subgoals.
The subproof is completed by applying H0.
Apply explicit_Field_zero_multR with
field0
x0
,
ap
(
Field_of_RealsStruct
x0
)
3
,
ap
(
Field_of_RealsStruct
x0
)
4
,
decode_b
(
ap
(
Field_of_RealsStruct
x0
)
1
)
,
decode_b
(
ap
(
Field_of_RealsStruct
x0
)
2
)
.
Apply explicit_Field_of_RealsStruct_2 with
x0
.
The subproof is completed by applying H0.
■