Let x0 of type ι → ι be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 x3 . x1 x3 x2 ⟶ x1 x3 (x0 x2).
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H1: x1 x3 x2.
Apply unknownprop_0cd951a82ebe4f4eae336dba1435eb57a5ebd8c7fea6487ca4fa5dfa1e00ce12 with
x0,
x1,
ChurchNum_ii_7 ChurchNum2 x0 x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_0cd951a82ebe4f4eae336dba1435eb57a5ebd8c7fea6487ca4fa5dfa1e00ce12 with
x0,
x1,
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.