Let x0 of type ι be given.
Apply unknownprop_aa42ade5598d8612d2029318c4ed81646c550ecc6cdd9ab953ce4bf73f3dd562 with
x0,
x0,
λ x1 . x1 leaving 2 subgoals.
The subproof is completed by applying unknownprop_780c037c813e255cbc58892be926cea515787b16c3205051ff8753787953a135 with x0.
Let x1 of type ι be given.
Let x2 of type ο be given.
Assume H1:
∀ x3 . and (In x3 x0) ((λ x4 . x4) x3 = x1) ⟶ x2.
Apply H1 with
x1.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
In x1 x0,
(λ x3 . x3) x1 = x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι → ι → ο be given.
Assume H2: x3 x1 x1.
The subproof is completed by applying H2.