Let x0 of type ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → CN (ι → ι) be given.
Let x1 of type ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → CN (ι → ι) be given.
Apply H0 with
λ x2 : ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ChurchNum_3ary_proj_p x1 ⟶ ChurchNum_3ary_proj_p (ChurchNums_8x3_to_3_lt7_id_ge7_rot2 x2 x1) leaving 8 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
The subproof is completed by applying H1.
Apply unknownprop_5881c3490ed9d7d79e8da4ec398853ff06374776f16caecd18fd5e637a25c01e with
x1.
The subproof is completed by applying H1.