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) ⟶ 28b0a.. x0 x2 = 28b0a.. x0 x1The subproof is completed by applying unknownprop_9e7ec4148d62bafcd9e146d1756f4a7aed7c3eb8fc00334b6fe1712064d0a901.
Claim L1:
∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ∈ x0) ⟶ 28b0a.. x0 x1 ⟶ ∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ x3 x4 x5 ∈ x2) ⟶ 28b0a.. 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) ⟶ 28b0a.. (setprod x0 x2) x4The subproof is completed by applying unknownprop_eaaabdc027024a28dc413cf5c8f24ae2d95c1cae5e12cd1597df72e68312adf2.
Apply unknownprop_d305e4f28748e3527529c751b716fb93c014046566c5ce2cf4a34b9f2fbe0cdc with
28b0a.. leaving 2 subgoals.
The subproof is completed by applying L0.
The subproof is completed by applying L1.