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Proofgold Proof

pf
Apply unknownprop_f04ee3f2db7dade92ee7be101bff40fb89f733bb0c0340f09b616cd72154ad93 with λ x0 . e6316.. x0 (4ae4a.. 4a7ef..) = x0.
Let x0 of type ι be given.
Assume H0: 80242.. x0.
Assume H1: ∀ x1 . prim1 x1 (56ded.. (e4431.. x0))e6316.. x1 (4ae4a.. 4a7ef..) = x1.
Apply unknownprop_0bba6b6e1ff88cb6fe93e4b3f72d170fee2180507070ff2fab0f5b4dc92e6b37 with x0, 4ae4a.. 4a7ef.., e6316.. x0 (4ae4a.. 4a7ef..) = x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying unknownprop_3d71b8748f06c73392acc73d46c8ae7fc07e5709a18169240b1cb765b8547148.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2: 02b90.. x1 x2.
Assume H3: ∀ x3 . prim1 x3 x1∀ x4 : ο . (∀ x5 . prim1 x5 (23e07.. x0)∀ x6 . prim1 x6 (23e07.. (4ae4a.. 4a7ef..))x3 = bc82c.. (e6316.. x5 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))x4)(∀ x5 . prim1 x5 (5246e.. x0)∀ x6 . prim1 x6 (5246e.. (4ae4a.. 4a7ef..))x3 = bc82c.. (e6316.. x5 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))x4)x4.
Assume H4: ∀ x3 . prim1 x3 (23e07.. x0)∀ x4 . prim1 x4 (23e07.. (4ae4a.. 4a7ef..))prim1 (bc82c.. (e6316.. x3 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x4) (f4dc0.. (e6316.. x3 x4)))) x1.
Assume H5: ∀ x3 . prim1 x3 (5246e.. x0)∀ x4 . prim1 x4 (5246e.. (4ae4a.. 4a7ef..))prim1 (bc82c.. (e6316.. x3 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x4) (f4dc0.. (e6316.. x3 x4)))) x1.
Assume H6: ∀ x3 . prim1 x3 x2∀ x4 : ο . (∀ x5 . prim1 x5 (23e07.. x0)∀ x6 . prim1 x6 (5246e.. (4ae4a.. 4a7ef..))x3 = bc82c.. (e6316.. x5 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))x4)(∀ x5 . prim1 x5 (5246e.. x0)∀ x6 . prim1 x6 (23e07.. (4ae4a.. 4a7ef..))x3 = bc82c.. (e6316.. x5 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x6) (f4dc0.. (e6316.. x5 x6)))x4)x4.
Assume H7: ∀ x3 . prim1 x3 (23e07.. x0)∀ x4 . prim1 x4 (5246e.. (4ae4a.. 4a7ef..))prim1 (bc82c.. (e6316.. x3 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x4) (f4dc0.. (e6316.. x3 x4)))) x2.
Assume H8: ∀ x3 . ...∀ x4 . prim1 ... ...prim1 (bc82c.. (e6316.. x3 (4ae4a.. 4a7ef..)) (bc82c.. (e6316.. x0 x4) (f4dc0.. (e6316.. x3 x4)))) x2.
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