Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι → ι be given.
Apply H0 with
λ x3 . x3 = b6bd3.. x0 x1 x2 ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 leaving 2 subgoals.
Let x3 of type ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ι be given.
Apply unknownprop_7f80ec3822be3c72deb8d67082e2ad00c541f16edb0690153a8f263ec09d639c with
x3,
x0,
x4,
x1,
x5,
x2,
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ prim1 (x1 x6 x7) x0 leaving 2 subgoals.
The subproof is completed by applying H3.
Assume H4:
and (x3 = x0) (∀ x6 . prim1 x6 x3 ⟶ ∀ x7 . prim1 x7 x3 ⟶ x4 x6 x7 = x1 x6 x7).
Apply H4 with
(∀ x6 . prim1 x6 x3 ⟶ ∀ x7 . prim1 x7 x3 ⟶ x5 x6 x7 = x2 x6 x7) ⟶ ∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ prim1 (x1 x6 x7) x0.
Assume H5: x3 = x0.
Assume H6:
∀ x6 . prim1 x6 x3 ⟶ ∀ x7 . prim1 x7 x3 ⟶ x4 x6 x7 = x1 x6 x7.
Assume H7:
∀ x6 . prim1 x6 x3 ⟶ ∀ x7 . prim1 x7 x3 ⟶ x5 x6 x7 = x2 x6 x7.
Apply H5 with
λ x6 x7 . ∀ x8 . prim1 x8 x6 ⟶ ∀ x9 . prim1 x9 x6 ⟶ prim1 (x1 x8 x9) x6.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply H6 with
x6,
x7,
λ x8 x9 . prim1 x8 x3 leaving 3 subgoals.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
Apply H1 with
x6,
x7 leaving 2 subgoals.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H1.