Let x0 of type ι → ο be given.
Assume H0:
(∀ x1 . not (x0 x1)) ⟶ False.
Apply unknownprop_b257b354d80b58d9a8444b167a21f47b4aabc910dc3698404491d5ef01e18cf3 with
x0 (Eps_i x0),
False leaving 2 subgoals.
Assume H2:
x0 (Eps_i x0).
Apply H1.
The subproof is completed by applying H2.
Apply H0.
Let x1 of type ι be given.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x0 x1.
Assume H3: x0 x1.
Apply notE with
x0 (Eps_i x0) leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_c3f0de4cb966012957ca752938aa96a32c594389e7aea45227d571c0506618ba with
x0,
x1.
The subproof is completed by applying H3.