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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type (ιο) → ο be given.
Let x2 of type ιι be given.
Let x3 of type ιιο be given.
Assume H0: 9a300.. (17e9f.. x0 x1 x2 x3).
Apply H0 with λ x4 . x4 = 17e9f.. x0 x1 x2 x3∀ x5 . prim1 x5 x0prim1 (x2 x5) x0 leaving 2 subgoals.
Let x4 of type ι be given.
Let x5 of type (ιο) → ο be given.
Let x6 of type ιι be given.
Assume H1: ∀ x7 . prim1 x7 x4prim1 (x6 x7) x4.
Let x7 of type ιιο be given.
Assume H2: 17e9f.. x4 x5 x6 x7 = 17e9f.. x0 x1 x2 x3.
Apply unknownprop_a07b205c3bf3848cdad7791d70b4ba425a8740a253f5b62fe8f647514df89904 with x4, x0, x5, x1, x6, x2, x7, x3, ∀ x8 . prim1 x8 x0prim1 (x2 x8) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: and (and (x4 = x0) (∀ x8 : ι → ο . (∀ x9 . x8 x9prim1 x9 x4)x5 x8 = x1 x8)) (∀ x8 . prim1 x8 x4x6 x8 = x2 x8).
Apply H3 with (∀ x8 . prim1 x8 x4∀ x9 . prim1 x9 x4x7 x8 x9 = x3 x8 x9)∀ x8 . prim1 x8 x0prim1 (x2 x8) x0.
Assume H4: and (x4 = x0) (∀ x8 : ι → ο . (∀ x9 . x8 x9prim1 x9 x4)x5 x8 = x1 x8).
Apply H4 with (∀ x8 . prim1 x8 x4x6 x8 = x2 x8)(∀ x8 . prim1 x8 x4∀ x9 . prim1 x9 x4x7 x8 x9 = x3 x8 x9)∀ x8 . prim1 x8 x0prim1 (x2 x8) x0.
Assume H5: x4 = x0.
Assume H6: ∀ x8 : ι → ο . (∀ x9 . x8 x9prim1 x9 x4)x5 x8 = x1 x8.
Assume H7: ∀ x8 . prim1 x8 x4x6 x8 = x2 x8.
Assume H8: ∀ x8 . prim1 x8 x4∀ x9 . prim1 x9 x4x7 x8 x9 = x3 x8 x9.
Apply H5 with λ x8 x9 . ∀ x10 . prim1 x10 x8prim1 (x2 x10) x8.
Let x8 of type ι be given.
Assume H9: prim1 x8 x4.
Apply H7 with x8, λ x9 x10 . prim1 x9 x4 leaving 2 subgoals.
The subproof is completed by applying H9.
Apply H1 with x8.
The subproof is completed by applying H9.
Let x4 of type ιιο be given.
Assume H1: x4 (17e9f.. x0 x1 x2 x3) (17e9f.. x0 x1 x2 x3).
The subproof is completed by applying H1.