Let x0 of type ο be given.
Let x1 of type ι → ι → ο be given.
Let x2 of type ι → ι → ο be given.
Assume H0: x0.
Apply functional extensionality with
a113b.. x0 x1 x2,
x1.
Let x3 of type ι be given.
Apply functional extensionality with
a113b.. x0 x1 x2 x3,
x1 x3.
Let x4 of type ι be given.
Apply prop_ext_2 with
a113b.. x0 x1 x2 x3 x4,
x1 x3 x4 leaving 2 subgoals.
Assume H1:
and (x0 ⟶ x1 x3 x4) (not x0 ⟶ x2 x3 x4).
Apply unknownprop_c29e201c2636d12615b11e1220001fcc0c2bbdeb53735eb34683c60a05a28860 with
x0 ⟶ x1 x3 x4,
not x0 ⟶ x2 x3 x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Assume H1: x1 x3 x4.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
x0 ⟶ x1 x3 x4,
not x0 ⟶ x2 x3 x4 leaving 2 subgoals.
Assume H2: x0.
The subproof is completed by applying H1.
Apply FalseE with
x2 x3 x4.
Apply notE with
x0 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H0.