Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι → ο be given.
Assume H0:
x0 = 1670d.. x1 x2 x3 x4.
Let x5 of type ι be given.
Apply H0 with
λ x6 x7 . x3 x5 = f482f.. (f482f.. x7 (4ae4a.. (4ae4a.. 4a7ef..))) x5.
Apply unknownprop_609acd0443eff633f33b94b7c15d47d918cf33a39d90a74bb85300ccecac83fa with
x1,
eb53d.. x1 x2,
0fc90.. x1 x3,
1216a.. x1 x4,
λ x6 x7 . x3 x5 = f482f.. x7 x5.
Let x6 of type ι → ι → ο be given.
Apply unknownprop_b456609235d152f08bccfce314d541d7c44f3716137c00b0ce21cf467ba83d17 with
x1,
x3,
x5,
λ x7 x8 . x6 x8 x7.
The subproof is completed by applying H1.