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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 explicit_OrderedField_E 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)))explicit_OrderedField x6 x7 x8 x9 x10 x11.
Assume H0: explicit_OrderedField x0 x1 x2 x3 x4 x5.
Apply explicit_Field_E with x0, x1, x2, x3, x4, (∀ x13 . ...∀ x14 . prim1 x14 ...∀ x15 . prim1 x15 x0x5 x13 x14x5 x14 x15x5 x13 x15)(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0iff (and (x5 x13 x14) (x5 x14 x13)) (x13 = x14))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0or (x5 x13 x14) (x5 x14 x13))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0∀ x15 . prim1 x15 x0x5 x13 x14x5 (x3 x13 x15) (x3 x14 x15))(∀ x13 . prim1 x13 x0∀ x14 . prim1 x14 x0x5 x1 x13x5 x1 x14x5 x1 (x4 x13 x14))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)))explicit_OrderedField x6 x7 x8 x9 x10 x11.
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