Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Apply unknownprop_1a2baecd136edc7de9ce039d67aaa286a9dcf8e2bec22b679c6c9114229bd217 with
λ x5 x6 : ι → ι → (ι → ι) → (ι → ι) → ι → ι . x6 x0 x1 x2 x3 (Inj1 x4) = x3 x4.
Apply unknownprop_56702b69fe31029117149136473717807c61136823145112690cf6c5e3fd3b5f with
x4,
λ x5 x6 . If_i (Inj1 x4 = Inj0 x6) (x2 x6) (x3 x6) = x3 x4.
Apply unknownprop_5a150bd86f4285de5d98c60b17d4452a655b4d88de0a02247259cdad6e6d992c with
Inj1 x4 = Inj0 x4,
x2 x4,
x3 x4.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
Inj1 x4 = Inj0 x4.
Apply notE with
Inj0 x4 = Inj1 x4 leaving 2 subgoals.
The subproof is completed by applying unknownprop_2909aa42e9d0a354d060bc7d707070a586f9ab4666ef2c2e92d5cb1072a37e98 with x4, x4.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H0 with λ x6 x7 . x5 x7 x6.