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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
IrreflexiveSymmetricReln
x0
.
Apply H0 with
struct_r
x0
.
Assume H1:
struct_r
x0
.
Assume H2:
unpack_r_o
x0
(
λ x1 .
λ x2 :
ι →
ι → ο
.
and
(
∀ x3 .
x3
∈
x1
⟶
not
(
x2
x3
x3
)
)
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
)
.
The subproof is completed by applying H1.
■