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Proofgold Proof

pf
Apply unknownprop_72dc8a048701bf51fd7b8ba6b7bf88eb6b499e1dce5a6cc41194ad4cd8a8616a with λ x0 . λ x1 : ι → ο . ∀ x2 : ο . (x0 = 5e331..x1 = 07017..x2)(∀ x3 x4 . ∀ x5 x6 : ι → ο . 858ff.. x3 x5858ff.. x4 x6x0 = a3eb9.. x3 x4x1 = c0709.. x5 x6x2)(∀ x3 x4 . ∀ x5 x6 : ι → ο . 858ff.. x3 x5858ff.. x4 x6x0 = bf68c.. x3 x4x1 = 6e020.. x5 x6x2)x2 leaving 3 subgoals.
Let x0 of type ο be given.
Assume H0: 5e331.. = 5e331..07017.. = 07017..x0.
Assume H1: ∀ x1 x2 . ∀ x3 x4 : ι → ο . 858ff.. x1 x3858ff.. x2 x45e331.. = a3eb9.. x1 x207017.. = c0709.. x3 x4x0.
Assume H2: ∀ x1 x2 . ∀ x3 x4 : ι → ο . 858ff.. x1 x3858ff.. x2 x45e331.. = bf68c.. x1 x207017.. = 6e020.. x3 x4x0.
Apply H0 leaving 2 subgoals.
Let x1 of type ιιο be given.
Assume H3: x1 5e331.. 5e331...
The subproof is completed by applying H3.
Let x1 of type (ιο) → (ιο) → ο be given.
Assume H3: x1 07017.. 07017...
The subproof is completed by applying H3.
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιο be given.
Let x3 of type ιο be given.
Assume H0: 858ff.. x0 x2.
Assume H1: ∀ x4 : ο . (x0 = 5e331..x2 = 07017..x4)(∀ x5 x6 . ∀ x7 x8 : ι → ο . 858ff.. x5 x7858ff.. x6 x8x0 = a3eb9.. x5 x6x2 = c0709.. x7 x8x4)(∀ x5 x6 . ∀ x7 x8 : ι → ο . 858ff.. x5 x7858ff.. x6 x8x0 = bf68c.. x5 x6x2 = 6e020.. x7 x8x4)x4.
Assume H2: 858ff.. x1 x3.
Assume H3: ∀ x4 : ο . (x1 = 5e331..x3 = 07017..x4)(∀ x5 x6 . ∀ x7 x8 : ι → ο . 858ff.. x5 x7858ff.. x6 x8x1 = a3eb9.. x5 x6x3 = c0709.. x7 x8x4)(∀ x5 x6 . ∀ x7 x8 : ι → ο . 858ff.. x5 x7858ff.. x6 x8x1 = bf68c.. x5 x6x3 = 6e020.. x7 x8x4)x4.
Let x4 of type ο be given.
Assume H4: a3eb9.. x0 x1 = 5e331..c0709.. x2 x3 = 07017..x4.
Assume H5: ∀ x5 x6 . ∀ x7 x8 : ι → ο . 858ff.. x5 x7858ff.. x6 x8a3eb9.. x0 x1 = a3eb9.. x5 x6c0709.. x2 x3 = c0709.. x7 x8x4.
Assume H6: ∀ x5 x6 . ∀ x7 x8 : ι → ο . ......a3eb9.. x0 x1 = bf68c.. x5 x6c0709.. x2 x3 = 6e020.. x7 x8x4.
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