Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Apply H0 with
λ x5 . x5 = ba600.. x0 x1 x2 x3 x4 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x6) x0 leaving 2 subgoals.
Let x5 of type ι be given.
Let x6 of type ι → ι be given.
Let x7 of type ι → ι be given.
Let x8 of type ι → ο be given.
Let x9 of type ι → ο be given.
Apply unknownprop_dfd4fae88bfedb56fcc54e334ca0f06b3233d70e71221a63438f303707186b2a with
x5,
x0,
x6,
x1,
x7,
x2,
x8,
x3,
x9,
x4,
∀ x10 . prim1 x10 x0 ⟶ prim1 (x1 x10) x0 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H4:
and (and (and (x5 = x0) (∀ x10 . prim1 x10 x5 ⟶ x6 x10 = x1 x10)) (∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10)) (∀ x10 . prim1 x10 x5 ⟶ x8 x10 = x3 x10).
Apply H4 with
(∀ x10 . prim1 x10 x5 ⟶ x9 x10 = x4 x10) ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x1 x10) x0.
Assume H5:
and (and (x5 = x0) (∀ x10 . prim1 x10 x5 ⟶ x6 x10 = x1 x10)) (∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10).
Apply H5 with
(∀ x10 . prim1 x10 x5 ⟶ x8 x10 = x3 x10) ⟶ (∀ x10 . prim1 x10 x5 ⟶ x9 x10 = x4 x10) ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x1 x10) x0.
Assume H6:
and (x5 = x0) (∀ x10 . prim1 x10 x5 ⟶ x6 x10 = x1 x10).
Apply H6 with
(∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10) ⟶ (∀ x10 . prim1 x10 x5 ⟶ x8 x10 = x3 x10) ⟶ (∀ x10 . prim1 x10 x5 ⟶ x9 x10 = x4 x10) ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x1 x10) x0.
Assume H7: x5 = x0.
Assume H8:
∀ x10 . prim1 x10 x5 ⟶ x6 x10 = x1 x10.
Assume H9:
∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10.
Assume H10:
∀ x10 . prim1 x10 x5 ⟶ x8 x10 = x3 x10.
Assume H11:
∀ x10 . prim1 ... ... ⟶ x9 x10 = x4 x10.