Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ο be given.
Apply H0 with
λ x3 . x3 = 73737.. x0 x1 x2 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x4) x0 leaving 2 subgoals.
Let x3 of type ι be given.
Let x4 of type ι → ι be given.
Let x5 of type ι → ι → ο be given.
Apply unknownprop_dd02d720bb2b5310cc2d2d04b51d8f171abb261812a3f85b1ce8eda4d35f73c7 with
x3,
x0,
x4,
x1,
x5,
x2,
∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x6) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3:
and (x3 = x0) (∀ x6 . prim1 x6 x3 ⟶ x4 x6 = x1 x6).
Apply H3 with
(∀ x6 . prim1 x6 x3 ⟶ ∀ x7 . prim1 x7 x3 ⟶ x5 x6 x7 = x2 x6 x7) ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x6) x0.
Assume H4: x3 = x0.
Assume H5:
∀ x6 . prim1 x6 x3 ⟶ x4 x6 = x1 x6.
Assume H6:
∀ x6 . prim1 x6 x3 ⟶ ∀ x7 . prim1 x7 x3 ⟶ x5 x6 x7 = x2 x6 x7.
Apply H4 with
λ x6 x7 . ∀ x8 . prim1 x8 x6 ⟶ prim1 (x1 x8) x6.
Let x6 of type ι be given.
Apply H5 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.