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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 ιιι be given.
Let x3 of type ιιο be given.
Let x4 of type ιιο be given.
Assume H0: 3d094.. (38265.. x0 x1 x2 x3 x4).
Apply H0 with λ x5 . x5 = 38265.. x0 x1 x2 x3 x4∀ x6 . prim1 x6 x0∀ x7 . prim1 x7 x0prim1 (x2 x6 x7) x0 leaving 2 subgoals.
Let x5 of type ι be given.
Let x6 of type (ιο) → ο be given.
Let x7 of type ιιι be given.
Assume H1: ∀ x8 . prim1 x8 x5∀ x9 . prim1 x9 x5prim1 (x7 x8 x9) x5.
Let x8 of type ιιο be given.
Let x9 of type ιιο be given.
Assume H2: 38265.. x5 x6 x7 x8 x9 = 38265.. x0 x1 x2 x3 x4.
Apply unknownprop_f00564205a7209895e36a1e928e17e3f73906bcc18f5405d51a9e35255d15f54 with x5, x0, x6, x1, x7, x2, x8, x3, x9, x4, ∀ x10 . prim1 x10 x0∀ x11 . prim1 x11 x0prim1 (x2 x10 x11) x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: and (and (and (x5 = x0) (∀ x10 : ι → ο . (∀ x11 . x10 x11prim1 x11 x5)x6 x10 = x1 x10)) (∀ x10 . prim1 x10 x5∀ x11 . prim1 x11 x5x7 x10 x11 = x2 x10 x11)) (∀ x10 . prim1 x10 x5∀ x11 . prim1 x11 x5x8 x10 x11 = x3 x10 x11).
Apply H3 with (∀ x10 . prim1 x10 x5∀ x11 . prim1 x11 x5x9 x10 x11 = x4 x10 x11)∀ x10 . prim1 x10 x0∀ x11 . prim1 x11 x0prim1 (x2 x10 x11) x0.
Assume H4: and (and (x5 = x0) (∀ x10 : ι → ο . (∀ x11 . x10 x11prim1 x11 x5)x6 x10 = x1 x10)) (∀ x10 . prim1 x10 x5∀ x11 . prim1 x11 x5x7 x10 x11 = x2 x10 x11).
Apply H4 with (∀ x10 . prim1 x10 x5∀ x11 . prim1 x11 x5x8 x10 x11 = x3 x10 x11)(∀ x10 . prim1 x10 x5∀ x11 . prim1 x11 x5x9 x10 x11 = x4 x10 x11)∀ x10 . prim1 x10 x0∀ x11 . prim1 x11 x0prim1 (x2 x10 x11) x0.
Assume H5: and (x5 = x0) (∀ x10 : ι → ο . (∀ x11 . x10 x11prim1 x11 x5)x6 x10 = x1 x10).
Apply H5 with .........∀ x10 . ...∀ x11 . prim1 x11 ...prim1 (x2 x10 x11) x0.
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