Let x0 of type ι → ο be given.
Assume H0:
∀ x1 . ba9d8.. x1 ⟶ (∀ x2 . prim1 x2 x1 ⟶ x0 x2) ⟶ x0 x1.
Apply unknownprop_85336ee07ace71a942dc508d3b8c851d9d6bb88511443b7dafbf11b71c263f4d with
λ x1 . ∀ x2 . prim1 x2 x1 ⟶ x0 x2 leaving 2 subgoals.
Let x1 of type ι be given.
Apply FalseE with
x0 x1.
Apply unknownprop_da3368fefc81e401e6446c98c0c04ab87d76d6f97c47fe5fd07c1e3c2f00ef6a with
x1.
The subproof is completed by applying H1.
Let x1 of type ι be given.
Assume H2:
∀ x2 . prim1 x2 x1 ⟶ x0 x2.
Let x2 of type ι be given.
Apply unknownprop_dec2978c0a72cebd51fcab0a380f03d4d80d1ccd8f826d378953148c305a60f0 with
x1,
x2,
x0 x2 leaving 3 subgoals.
The subproof is completed by applying H3.
Apply H2 with
x2.
The subproof is completed by applying H4.
Assume H4: x2 = x1.
Apply H4 with
λ x3 x4 . x0 x4.
Apply H0 with
x1 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x1 of type ι be given.
Apply H0 with
x1 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply L1 with
x1.
The subproof is completed by applying H2.