Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Apply H0 with
4f2b4.. (987b2.. x0 x1).
Assume H1:
and (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4).
Apply H1 with
(∃ x2 . and (prim1 x2 x0) (and (∀ x3 . prim1 x3 x0 ⟶ and (x1 x2 x3 = x3) (x1 x3 x2 = x3)) (∀ x3 . prim1 x3 x0 ⟶ ∃ x4 . and (prim1 x4 x0) (and (x1 x3 x4 = x2) (x1 x4 x3 = x2))))) ⟶ 4f2b4.. (987b2.. x0 x1).
Assume H3:
∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x2 (x1 x3 x4) = x1 (x1 x2 x3) x4.
Assume H4:
∃ x2 . and (prim1 x2 x0) (and (∀ x3 . prim1 x3 x0 ⟶ and (x1 x2 x3 = x3) (x1 x3 x2 = x3)) (∀ x3 . prim1 x3 x0 ⟶ ∃ x4 . and (prim1 x4 x0) (and (x1 x3 x4 = x2) (x1 x4 x3 = x2)))).
Apply andI with
30750.. (987b2.. x0 x1),
93c99.. (987b2.. x0 x1) explicit_Group leaving 2 subgoals.
Apply unknownprop_10272f9d8a272cf914054010d8c3a4593cfbbcb7954b0a903e2d867e85e26e68 with
x0,
x1.
The subproof is completed by applying H2.
Apply unknownprop_6881ac7ad4356c09fff02e0a39d3a1d9923586474092567f0c58da443f0e8918 with
x0,
x1,
λ x2 x3 : ο . x3.
The subproof is completed by applying H0.