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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 (ιο) → ο be given.
Let x3 of type ιι be given.
Let x4 of type ιι be given.
Let x5 of type ιιο be given.
Let x6 of type ιιο be given.
Assume H0: ∀ x7 : ι → ο . (∀ x8 . x7 x8prim1 x8 x0)iff (x1 x7) (x2 x7).
Assume H1: ∀ x7 . prim1 x7 x0x3 x7 = x4 x7.
Assume H2: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0iff (x5 x7 x8) (x6 x7 x8).
Claim L3: ...
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Apply L3 with λ x7 x8 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x3) (d2155.. x0 x5)))) = 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x7 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x4) (d2155.. x0 x6)))).
Claim L4: ...
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Apply L4 with λ x7 x8 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x3) (d2155.. x0 x5)))) = 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x7 (d2155.. x0 x6)))).
Claim L5: ...
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Apply L5 with λ x7 x8 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x3) (d2155.. x0 x5)))) = 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x3) x7))).
Let x7 of type ιιο be given.
Assume H6: x7 (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x8 . If_i (x8 = 4a7ef..) x0 (If_i (x8 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x8 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 ...) ...)))) ....
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