Let x0 of type ο be given.
Let x1 of type ο be given.
Let x2 of type ο be given.
Assume H1: x0 ⟶ x1 ⟶ x2.
Assume H2:
not x0 ⟶ not x1 ⟶ x2.
Apply andE with
x0 ⟶ x1,
x1 ⟶ x0,
x2 leaving 2 subgoals.
Apply unknownprop_535a42de1055bca61f176bc11115db76b3356ad18505799408acb5bdbd2addc1 with
λ x3 x4 : ο → ο → ο . x3 x0 x1.
The subproof is completed by applying H0.
Assume H3: x0 ⟶ x1.
Assume H4: x1 ⟶ x0.
Apply unknownprop_b257b354d80b58d9a8444b167a21f47b4aabc910dc3698404491d5ef01e18cf3 with
x0,
x2 leaving 2 subgoals.
Assume H5: x0.
Apply H1 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply H3.
The subproof is completed by applying H5.
Apply H2 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
x1.
Assume H6: x1.
Apply notE with
x0 leaving 2 subgoals.
The subproof is completed by applying H5.
Apply H4.
The subproof is completed by applying H6.