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 x5 . MagmaHom (pack_b x0 x1) (pack_b x2 x3) x4 ⟶ MagmaHom (pack_b x0 x1) (pack_b x2 x3) x5 ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . x7 ∈ {x8 ∈ x0|ap x4 x8 = ap x5 x8} ⟶ ∀ x8 . x8 ∈ {x9 ∈ x0|ap x4 x9 = ap x5 x9} ⟶ x1 x7 x8 = x6 x7 x8) ⟶ 28b0a.. {x7 ∈ x0|ap x4 x7 = ap x5 x7} x6The subproof is completed by applying unknownprop_877c0f5e4051c0b1f34b0b06bbae6dace9e6ec6fb22c5fc4b6ec8835e23b76b4.
Apply unknownprop_cffd5c2c6377c7c9139709f837f7b00ba99be51fbf6add4c20b3723106916eaa with
28b0a.. leaving 2 subgoals.
The subproof is completed by applying L0.
The subproof is completed by applying L1.