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.
Let x3 of type ι → ι be given.
Let x4 of type ι → ι be given.
Apply H0 with
λ x5 . x5 = 37dbe.. x0 x1 x2 x3 x4 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x4 x6) x0 leaving 2 subgoals.
Let x5 of type ι be given.
Let x6 of type ι → ι → ι be given.
Let x7 of type ι → ι → ι be given.
Let x8 of type ι → ι be given.
Let x9 of type ι → ι be given.
Assume H4:
∀ x10 . prim1 x10 x5 ⟶ prim1 (x9 x10) x5.
Apply unknownprop_eeb97a59839784c491ec977f7e1c65dccc23e8d5900a983d2b55d73c291fe0ba with
x5,
x0,
x6,
x1,
x7,
x2,
x8,
x3,
x9,
x4,
∀ x10 . prim1 x10 x0 ⟶ prim1 (x4 x10) x0 leaving 2 subgoals.
The subproof is completed by applying H5.
Assume H6:
and (and (and (x5 = x0) (∀ x10 . prim1 x10 x5 ⟶ ∀ x11 . prim1 x11 x5 ⟶ x6 x10 x11 = x1 x10 x11)) (∀ x10 . prim1 x10 x5 ⟶ ∀ x11 . prim1 x11 x5 ⟶ x7 x10 x11 = x2 x10 x11)) (∀ x10 . prim1 x10 x5 ⟶ x8 x10 = x3 x10).
Apply H6 with
(∀ x10 . prim1 x10 x5 ⟶ x9 x10 = x4 x10) ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x4 x10) x0.
Assume H7:
and (and (x5 = x0) (∀ x10 . prim1 x10 x5 ⟶ ∀ x11 . prim1 x11 x5 ⟶ x6 x10 x11 = x1 x10 x11)) (∀ x10 . prim1 x10 x5 ⟶ ∀ x11 . prim1 x11 x5 ⟶ x7 x10 x11 = x2 x10 x11).
Apply H7 with
(∀ x10 . prim1 x10 x5 ⟶ x8 x10 = x3 x10) ⟶ (∀ x10 . prim1 x10 x5 ⟶ x9 x10 = x4 x10) ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x4 x10) x0.
Assume H8:
and (x5 = x0) (∀ x10 . prim1 x10 x5 ⟶ ∀ x11 . prim1 x11 x5 ⟶ x6 x10 x11 = x1 x10 x11).
Apply H8 with
... ⟶ ... ⟶ (∀ x10 . ... ⟶ x9 x10 = x4 x10) ⟶ ∀ x10 . prim1 x10 x0 ⟶ prim1 (x4 x10) x0.