Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ο be given.
Assume H0:
In x0 x1 ⟶ x2.
Assume H1:
nIn x0 x1 ⟶ x2.
Apply unknownprop_b257b354d80b58d9a8444b167a21f47b4aabc910dc3698404491d5ef01e18cf3 with
In x0 x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H2:
not (In x0 x1).
Apply H1.
Apply unknownprop_3ec14466ed0aaeda1a16471c7d77d44ee3048fda5177bf110947a6b334a3fea0 with
x0,
x1.
The subproof is completed by applying H2.