Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Apply H0 with
λ x2 . x2 = 987b2.. x0 x1 ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x3 x4) x0 leaving 2 subgoals.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Apply unknownprop_5cd05a110f3bf2a31b9390cadb44d05e7c4e54bd01cb3a1cbe102c4d216d9b84 with
x2,
x0,
x3,
x1,
∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: x2 = x0.
Assume H4:
∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ x3 x4 x5 = x1 x4 x5.
Apply H3 with
λ x4 x5 . ∀ x6 . prim1 x6 x4 ⟶ ∀ x7 . prim1 x7 x4 ⟶ prim1 (x1 x6 x7) x4.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply H4 with
x4,
x5,
λ x6 x7 . prim1 x6 x2 leaving 3 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
Apply H1 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
Let x2 of type ι → ι → ο be given.
The subproof is completed by applying H1.