Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Let x2 of type ι → ι be given.
Apply H0 with
λ x3 . x3 = 971d3.. 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 → ι → ι be given.
Let x5 of type ι → ι be given.
Apply unknownprop_f3a122873bb16d0c343b40d8a72e2ca4a76b344a351a34c2345c94a419a626d8 with
x3,
x0,
x4,
x1,
x5,
x2,
∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x6) 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 ⟶ x5 x6 = x2 x6) ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x6) 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 ⟶ x5 x6 = x2 x6.
Apply H5 with
λ x6 x7 . ∀ x8 . prim1 x8 x6 ⟶ prim1 (x2 x8) x6.
Let x6 of type ι be given.
Apply H7 with
x6,
λ x7 x8 . prim1 x7 x3 leaving 2 subgoals.
The subproof is completed by applying H8.
Apply H2 with
x6.
The subproof is completed by applying H8.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H1.