Let x0 of type ι → ι → ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H0:
not (x0 x1 x3 = x0 x2 x4).
Apply H1.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x1 = x2.
Assume H3: x1 = x2.
Apply H2.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x3 = x4.
Assume H4: x3 = x4.
Apply notE with
x0 x1 x3 = x0 x2 x4 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply f_eq_i_i with
x0,
x1,
x2,
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.