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.
Apply H0 with
λ x4 . x4 = eb2d9.. x0 x1 x2 x3 ⟶ prim1 x3 x0 leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type (ι → ο) → ο be given.
Let x6 of type ι → ι be given.
Let x7 of type ι be given.
Apply unknownprop_66153c4dc667ad589414d276ae8e920a7895bf35e295ff08c42dfc61b4014a34 with
x4,
x0,
x5,
x1,
x6,
x2,
x7,
x3,
prim1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H4:
and (and (x4 = x0) (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x4) ⟶ x5 x8 = x1 x8)) (∀ x8 . prim1 x8 x4 ⟶ x6 x8 = x2 x8).
Apply H4 with
x7 = x3 ⟶ prim1 x3 x0.
Assume H5:
and (x4 = x0) (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x4) ⟶ x5 x8 = x1 x8).
Apply H5 with
(∀ x8 . prim1 x8 x4 ⟶ x6 x8 = x2 x8) ⟶ x7 = x3 ⟶ prim1 x3 x0.
Assume H6: x4 = x0.
Assume H7:
∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x4) ⟶ x5 x8 = x1 x8.
Assume H8:
∀ x8 . prim1 x8 x4 ⟶ x6 x8 = x2 x8.
Assume H9: x7 = x3.
Apply H6 with
λ x8 x9 . prim1 x3 x8.
Apply H9 with
λ x8 x9 . prim1 x8 x4.
The subproof is completed by applying H2.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H1.