Let x0 of type ι → (ι → ι → ι → ι) → ι → ι → ι be given.
Assume H0:
∀ x1 . ∀ x2 x3 : ι → ι → ι → ι . (∀ x4 . In x4 x1 ⟶ x2 x4 = x3 x4) ⟶ x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Apply unknownprop_a88159a7ab366b8736dd3edc174eb90d0f6c3dce33f5f2e38d1ba66209147e31 with
x0,
x1,
28408.. x0 x1,
x0 x1 (28408.. x0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_daaf8ce3957664fcbc487b80c957d9d575ea67bc77e2f725d70fb99664e9182c with
x0,
x1.
The subproof is completed by applying H0.
Apply unknownprop_83244b0a84fab14b04652d4ce0e1b741a5449097aa4d034697efa48f2907da45 with
x0,
x1.
The subproof is completed by applying H0.