Claim L0:
∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ∈ x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ x1 x3 x4 = x2 x3 x4) ⟶ explicit_Group x0 x2 = explicit_Group x0 x1Let x0 of type ι be given.
Let x1 of type ι → ι → ι be given.
Assume H0: ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ∈ x0.
The subproof is completed by applying unknownprop_7cb998e320926464e72b55fe938acb0cde0a2ed7c6dff5911366b099cfe694a7 with x0, x1.
Claim L1:
∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ∈ x0) ⟶ explicit_Group x0 x1 ⟶ ∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ∈ x2) ⟶ explicit_Group x2 x3 ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . x5 ∈ setprod x0 x2 ⟶ ∀ x6 . x6 ∈ setprod x0 x2 ⟶ lam 2 (λ x7 . If_i (x7 = 0) (x1 (ap x5 0) (ap x6 0)) (x3 (ap x5 1) (ap x6 1))) = x4 x5 x6) ⟶ explicit_Group (setprod x0 x2) x4The subproof is completed by applying unknownprop_b94c81a80692cb6780c85e4ec6b658129aab5c4a1429b0045f10cd072e8bf363.
Apply unknownprop_d305e4f28748e3527529c751b716fb93c014046566c5ce2cf4a34b9f2fbe0cdc with
explicit_Group leaving 2 subgoals.
The subproof is completed by applying L0.
The subproof is completed by applying L1.