Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: x0 = x1.
Assume H1:
not (x2 = x3).
Apply H2 leaving 2 subgoals.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x0 = x2.
Assume H4: x0 = x2.
Apply H3 leaving 2 subgoals.
Apply H4 with
λ x4 x5 . not (x5 = x3).
The subproof is completed by applying H1.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x1 = x3.
Assume H5: x1 = x3.
Apply notE with
x2 = x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H4 with
λ x4 x5 . x4 = x3.
Apply H5 with
λ x4 x5 . x0 = x4.
The subproof is completed by applying H0.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x1 = x2.
Assume H4: x1 = x2.
Apply H3 leaving 2 subgoals.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x0 = x3.
Assume H5: x0 = x3.
Apply notE with
x2 = x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H4 with
λ x4 x5 . x4 = x3.
Apply H5 with
λ x4 x5 . x1 = x4.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H0 with λ x5 x6 . x4 x6 x5.
Apply H4 with
λ x4 x5 . not (x5 = x3).
The subproof is completed by applying H1.