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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ιιι be given.
Let x4 of type ιιι be given.
Let x5 of type ιιο be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ιιι be given.
Let x10 of type ιιι be given.
Let x11 of type ιιο be given.
Let x12 of type ιι be given.
Apply unknownprop_6506e7f62d1e2e82dd2eb322e79d587cc72544941960f50f6323eafe1cce767a with x0, x1, x2, x3, x4, x5, bij x0 x6 x12x12 x1 = x7x12 x2 = x8(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0x12 (x3 x13 x14) = x9 (x12 x13) (x12 x14))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0x12 (x4 x13 x14) = x10 (x12 x13) (x12 x14))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0iff (x5 x13 x14) (x11 (x12 x13) (x12 x14)))62ee1.. x6 x7 x8 x9 x10 x11.
Assume H0: 62ee1.. x0 x1 x2 x3 x4 x5.
Apply explicit_OrderedField_E with x0, x1, x2, x3, x4, x5, ...(∀ x13 . prim1 x13 (b5c9f.. x0 (1216a.. x0 (natOfOrderedField_p x0 ... ... ... ... ...)))∀ x14 . prim1 x14 (b5c9f.. x0 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)))(∀ x15 . prim1 x15 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5))and (and (x5 (f482f.. x13 x15) (f482f.. x14 x15)) (x5 (f482f.. x13 x15) (f482f.. x13 (x3 x15 x2)))) (x5 (f482f.. x14 (x3 x15 x2)) (f482f.. x14 x15)))∃ x15 . and (prim1 x15 x0) (∀ x16 . prim1 x16 (1216a.. x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5))and (x5 (f482f.. x13 x16) x15) (x5 x15 (f482f.. x14 x16))))bij x0 x6 x12x12 x1 = x7x12 x2 = x8(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0x12 (x3 x13 x14) = x9 (x12 x13) (x12 x14))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0x12 (x4 x13 x14) = x10 (x12 x13) (x12 x14))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0iff (x5 x13 x14) (x11 (x12 x13) (x12 x14)))62ee1.. x6 x7 x8 x9 x10 x11.
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