Let x0 of type ι be given.
Let x1 of type (ι → ο) → ο be given.
Let x2 of type ι → ι be given.
Apply H0 with
λ x3 . x3 = fc7e7.. x0 x1 x2 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 leaving 2 subgoals.
Let x3 of type ι be given.
Let x4 of type (ι → ο) → ο be given.
Let x5 of type ι → ι be given.
Apply unknownprop_3e3b8f1601141efe5e4771ff7077d64ce391fe1e7da6996e4a598a59fea1a33b with
x3,
x0,
x4,
x1,
x5,
x2,
∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x6) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3:
and (x3 = x0) (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x3) ⟶ x4 x6 = x1 x6).
Apply H3 with
(∀ x6 . prim1 x6 x3 ⟶ x5 x6 = x2 x6) ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x6) x0.
Assume H4: x3 = x0.
Assume H5:
∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x3) ⟶ x4 x6 = x1 x6.
Assume H6:
∀ x6 . prim1 x6 x3 ⟶ x5 x6 = x2 x6.
Apply H4 with
λ x6 x7 . ∀ x8 . prim1 x8 x6 ⟶ prim1 (x2 x8) x6.
Let x6 of type ι be given.
Apply H6 with
x6,
λ x7 x8 . prim1 x7 x3 leaving 2 subgoals.
The subproof is completed by applying H7.
Apply H1 with
x6.
The subproof is completed by applying H7.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H1.