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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιο be given.
Let x2 of type ιο be given.
Let x3 of type ι be given.
Assume H0: 60280.. (e4ab3.. x0 x1 x2 x3).
Apply H0 with λ x4 . x4 = e4ab3.. x0 x1 x2 x3prim1 x3 x0 leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type ιιο be given.
Let x6 of type ιο be given.
Let x7 of type ι be given.
Assume H1: prim1 x7 x4.
Assume H2: e4ab3.. x4 x5 x6 x7 = e4ab3.. x0 x1 x2 x3.
Apply unknownprop_0537a1e724877bc55ca07fba8b1d9ee408039aab66986f05c35181eae5c10ebc with x4, x0, x5, x1, x6, x2, x7, x3, prim1 x3 x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: and (and (x4 = x0) (∀ x8 . prim1 x8 x4∀ x9 . prim1 x9 x4x5 x8 x9 = x1 x8 x9)) (∀ x8 . prim1 x8 x4x6 x8 = x2 x8).
Apply H3 with x7 = x3prim1 x3 x0.
Assume H4: and (x4 = x0) (∀ x8 . prim1 x8 x4∀ x9 . prim1 x9 x4x5 x8 x9 = x1 x8 x9).
Apply H4 with (∀ x8 . prim1 x8 x4x6 x8 = x2 x8)x7 = x3prim1 x3 x0.
Assume H5: x4 = x0.
Assume H6: ∀ x8 . prim1 x8 x4∀ x9 . prim1 x9 x4x5 x8 x9 = x1 x8 x9.
Assume H7: ∀ x8 . prim1 x8 x4x6 x8 = x2 x8.
Assume H8: x7 = x3.
Apply H5 with λ x8 x9 . prim1 x3 x8.
Apply H8 with λ x8 x9 . prim1 x8 x4.
The subproof is completed by applying H1.
Let x4 of type ιιο be given.
Assume H1: x4 (e4ab3.. x0 x1 x2 x3) (e4ab3.. x0 x1 x2 x3).
The subproof is completed by applying H1.