Let x0 of type ι be given.
Let x1 of type (ι → ο) → ο be given.
Let x2 of type ι → ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Apply H0 with
λ x5 . x5 = 9d1fa.. x0 x1 x2 x3 x4 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x6) x0 leaving 2 subgoals.
Let x5 of type ι be given.
Let x6 of type (ι → ο) → ο be given.
Let x7 of type ι → ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Apply unknownprop_b4350a2c477b5dff89a0f89fe026d38a5bc73b44962f85afe05a340e9f4088a7 with
x5,
x0,
x6,
x1,
x7,
x2,
x8,
x3,
x9,
x4,
∀ x10 . prim1 x10 x0 ⟶ prim1 (x2 x10) x0 leaving 2 subgoals.
The subproof is completed by applying H4.
Assume H5:
and (and (and (x5 = x0) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x5) ⟶ x6 x10 = x1 x10)) (∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10)) (x8 = x3).
Apply H5 with
x9 = x4 ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x2 x10) x0.
Assume H6:
and (and (x5 = x0) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x5) ⟶ x6 x10 = x1 x10)) (∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10).
Apply H6 with
x8 = x3 ⟶ x9 = x4 ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x2 x10) x0.
Assume H7:
and (x5 = x0) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x5) ⟶ x6 x10 = x1 x10).
Apply H7 with
(∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10) ⟶ x8 = x3 ⟶ x9 = x4 ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x2 x10) x0.
Assume H8: x5 = x0.
Assume H9:
∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x5) ⟶ x6 x10 = x1 x10.
Assume H10:
∀ x10 . prim1 x10 x5 ⟶ x7 x10 = x2 x10.
Assume H11: x8 = x3.
Assume H12: x9 = x4.
Apply H8 with
λ x10 x11 . ∀ x12 . prim1 x12 x10 ⟶ prim1 (x2 x12) x10.
Let x10 of type ι be given.
Assume H13:
prim1 x10 x5.
Apply H10 with
x10,
λ x11 x12 . prim1 x11 x5 leaving 2 subgoals.
The subproof is completed by applying H13.
Apply H1 with
x10.
The subproof is completed by applying H13.
Let x5 of type ι → ι → ο be given.
Assume H1:
x5 (9d1fa.. x0 x1 x2 ... ...) ....