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Proofgold Signed Transaction

vin
PrRqB../0e80e..
PUhTp../cf60e..
vout
PrRqB../44832.. 24.98 bars
TMW7h../31c7e.. ownership of e3077.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYma../dde11.. ownership of 62b27.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbda../4cfe7.. ownership of ef0c5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVbP../8ff8b.. ownership of 1acb5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXE4../f4ac5.. ownership of 1ebb1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdVU../32fbe.. ownership of d70c5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVar../dcf3b.. ownership of 9ac35.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXv9../d4699.. ownership of de069.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHrQ../08ad9.. ownership of 883af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV5s../efe57.. ownership of bc8a3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFeS../49def.. ownership of 927ff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFzU../8d2ff.. ownership of 8e7dc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW1R../f1e9f.. ownership of 74507.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPs9../5297a.. ownership of 58cc1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc3H../0680f.. ownership of 27a4d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW8P../8ac6a.. ownership of bd9cd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaZj../24e5f.. ownership of 171bb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHEc../fbbb4.. ownership of efd5b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ8C../825f7.. ownership of ca10d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSrD../90236.. ownership of 571e9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHuT../7a25a.. ownership of a524c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLLE../a95af.. ownership of 94d5d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWu5../9f8d8.. ownership of 3e984.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRzz../d9692.. ownership of b5095.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNzM../aba0d.. ownership of 0ad90.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHf8../56e02.. ownership of b3896.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJbm../3597c.. ownership of 9f953.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdRK../aade4.. ownership of 892e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMazG../cddf7.. ownership of 25129.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR9G../67a1d.. ownership of bd7df.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWbY../5bfe2.. ownership of a7a18.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJAe../2b3a4.. ownership of f767a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW4c../e1f47.. ownership of 8411e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKjr../4bc0e.. ownership of 0cf25.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUts../39c15.. ownership of 4e843.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZCj../979c5.. ownership of 7bf62.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcoF../01fb6.. ownership of c8389.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbsF../271ed.. ownership of 2ba50.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaos../52e2f.. ownership of ba51b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWzf../ffcde.. ownership of 1174d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb3q../14ecf.. ownership of 407c2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaML../067d6.. ownership of d7c0a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFym../f1ed8.. ownership of fcffe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX6B../1dc73.. ownership of f1de2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYPz../98e06.. ownership of 4ac71.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMFj../6d945.. ownership of 653f7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYDr../7d536.. ownership of 48143.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZxW../0d6d1.. ownership of aedd4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbGx../e743c.. ownership of 89c28.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdQP../6aed7.. ownership of 6a5a6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHZg../04028.. ownership of aa92f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUkn../38b01.. ownership of 68fa4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMckR../6b82a.. ownership of 26708.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP3a../b2620.. ownership of 8aeb1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdaD../1363a.. ownership of 25e5a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcEe../061bc.. ownership of a2cc3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYiQ../a49b9.. ownership of ba1ae.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN3Q../c0aba.. ownership of 77b58.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUmh../436cc.. ownership of 96a2a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTtA../74c0b.. ownership of 3b64a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJu2../f3e93.. ownership of 17548.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaRi../c6cf6.. ownership of a73fd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd8i../cebe9.. ownership of 88c0b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXqw../91ad0.. ownership of f126e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMcQ../8cdf2.. ownership of 7790e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMExA../0bb87.. ownership of 26e9d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKaV../d8657.. ownership of c8bfe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXG9../16ef0.. ownership of 97c6f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLEL../d4d9a.. ownership of 588b8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUKe../15b80.. ownership of 5dace.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQku../c6ddc.. ownership of 86d05.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZqc../0dce4.. ownership of 4ff83.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaKB../69c56.. ownership of 46ace.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTPS../59510.. ownership of b51af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRKR../b9539.. ownership of 5cc48.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMvg../40745.. ownership of f0b8a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGBE../4ca5d.. ownership of d5c55.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUTb../42f41.. ownership of 430a2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRCf../cd754.. ownership of f0c4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQT6../9dbc4.. ownership of fde8f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPC1../cdddc.. ownership of f7410.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcte../f3501.. ownership of c9a4c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNde../e534f.. ownership of 642f0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFCi../fb430.. ownership of 66e0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK7e../5b9bb.. ownership of 9b43e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML6H../3b318.. ownership of 7fdf8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFnc../e0fe9.. ownership of 8f958.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMsY../980f9.. ownership of cdb10.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXi6../2f54a.. ownership of 8cbc4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRgm../83c16.. ownership of 73ba3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTrF../b8207.. ownership of 73d5c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNv8../f3ef9.. ownership of 45b26.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMBh../15c72.. ownership of c6202.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMyo../5aaec.. ownership of 65af4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJDT../7c330.. ownership of 1d5e4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMc5../23a1d.. ownership of 215f6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYcG../bc4a3.. ownership of 30c75.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLtK../d2300.. ownership of 58d19.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWm9../bdae0.. ownership of e72e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRUE../612da.. ownership of a3586.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ4H../a6eea.. ownership of 104bb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb4R../1ca2d.. ownership of 6da1e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNWV../e9cd8.. ownership of 5ef4c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWep../431d4.. ownership of 260af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMDr../b861b.. ownership of e41cf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWFg../1de5c.. ownership of 879ec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdK2../07335.. ownership of bb961.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRgC../55a72.. ownership of b8b91.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdXm../9f9d3.. ownership of 08a4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLMr../1e2fc.. ownership of c2e0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLWk../bb5ed.. ownership of 96b84.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRj7../6934a.. ownership of 25e2c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHTj../026a2.. ownership of 9800a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJN4../79a00.. ownership of 77e26.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMazk../c8bef.. ownership of da688.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWJj../b4a3f.. ownership of b723f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHYw../173dd.. ownership of 210e9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMSu../eec35.. ownership of e6daa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHsB../e3dca.. ownership of 2dc4f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU7B../86d3e.. ownership of b4350.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGzg../f6198.. ownership of ab3ea.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaVT../fb062.. ownership of 6c301.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFo9../d412a.. ownership of c15ab.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcsM../7a655.. ownership of 01953.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUFZ../8687a.. ownership of b5765.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQAk../66d4d.. ownership of 906b3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML3j../e2c8a.. ownership of 95d5a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPJN../1a164.. ownership of bf97f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRZE../c2475.. ownership of 72d9a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGQk../13741.. ownership of be48f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGjc../d3e54.. ownership of a916b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcst../56f97.. ownership of 583fe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUgt../694c9.. ownership of 12d1a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVKw../f15f1.. ownership of ea899.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWxt../4c6bc.. ownership of ce04c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLLa../eea7d.. ownership of 3f267.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTco../b6132.. ownership of a3ad9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRyg../b5bb2.. ownership of ed879.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR33../f8d19.. ownership of 73929.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYT5../a215e.. ownership of 12790.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTRo../b1d23.. ownership of d8a7a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQKs../6f7e3.. ownership of 2977b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQqx../3fc62.. ownership of 0fef8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHdp../3d14a.. ownership of 07316.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN9L../f86dc.. ownership of 781e8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcZu../49466.. ownership of d2f86.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJEp../fdaf6.. ownership of fe7e3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK8a../a5f0b.. ownership of aace9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGTJ../82dfa.. ownership of 2bfcf.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUQa../46644.. ownership of 6266c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFTR../4e3ce.. ownership of 8f423.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbxj../6afa5.. ownership of c2c9d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT8Z../3ea35.. ownership of db61c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSc3../e5e32.. ownership of 07717.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF7c../8ada9.. ownership of a3459.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF4f../f56d0.. ownership of 19670.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN4a../160ba.. ownership of 97de1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcPi../be82e.. ownership of 7cd48.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPLE../d04ae.. ownership of 4f31d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcQZ../bdc5a.. ownership of 75081.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMavu../bd54a.. ownership of 3030f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGfr../ea917.. ownership of a3d5f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPU7../b780b.. ownership of e6f8c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFrV../db7ba.. ownership of 6913a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM1w../ebce6.. ownership of 64bec.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXFv../48fad.. ownership of dafe9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHEB../67e84.. ownership of ac684.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYbW../6b44b.. ownership of 057c5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV8A../98844.. ownership of 9d3f2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbEX../4572d.. ownership of 685db.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWuB../37a67.. ownership of 9d1fa.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRvK../620bb.. ownership of 26208.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUNaV../a0ed6.. doc published by PrGxv..
Param 0fc90.. : ι → (ι → ι) → ι
Param 4ae4a.. : ι → ι
Param 4a7ef.. : ι
Param If_i : ο → ι → ι → ι
Param e0e40.. : ι → ((ι → ο) → ο) → ι
Definition 9d1fa.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι . λ x3 x4 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))
Param f482f.. : ι → ι → ι
Known 7d2e2.. : ∀ x0 x1 x2 x3 x4 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) x1 (If_i (x6 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x6 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))) 4a7ef.. = x0
Theorem 73929.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9d1fa.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem a3ad9.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . x0 = f482f.. (9d1fa.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Param decode_c : ι → (ι → ο) → ο
Known 504a8.. : ∀ x0 x1 x2 x3 x4 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) x1 (If_i (x6 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x6 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))) (4ae4a.. 4a7ef..) = x1
Known 81500.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . (∀ x3 . x2 x3 ⟶ prim1 x3 x0) ⟶ decode_c (e0e40.. x0 x1) x2 = x1 x2
Theorem ce04c.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9d1fa.. x1 x2 x3 x4 x5 ⟶ ∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ x2 x6 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem 12d1a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (9d1fa.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Known fb20c.. : ∀ x0 x1 x2 x3 x4 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) x1 (If_i (x6 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x6 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))) (4ae4a.. (4ae4a.. 4a7ef..)) = x2
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem a916b.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9d1fa.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 72d9a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (9d1fa.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Known 431f3.. : ∀ x0 x1 x2 x3 x4 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) x1 (If_i (x6 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x6 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x3
Theorem 95d5a.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9d1fa.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem b5765.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . x3 = f482f.. (9d1fa.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Known ffdcd.. : ∀ x0 x1 x2 x3 x4 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x6 . If_i (x6 = 4a7ef..) x0 (If_i (x6 = 4ae4a.. 4a7ef..) x1 (If_i (x6 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x6 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x4
Theorem c15ab.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9d1fa.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem ab3ea.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . x4 = f482f.. (9d1fa.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known and5I : ∀ x0 x1 x2 x3 x4 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ and (and (and (and x0 x1) x2) x3) x4
Theorem 2dc4f.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . ∀ x6 x7 x8 x9 . 9d1fa.. x0 x2 x4 x6 x8 = 9d1fa.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10)) (x6 = x7)) (x8 = x9) (proof)
Param iff : ο → ο → ο
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Known fe043.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . (∀ x3 : ι → ο . (∀ x4 . x3 x4 ⟶ prim1 x4 x0) ⟶ iff (x1 x3) (x2 x3)) ⟶ e0e40.. x0 x1 = e0e40.. x0 x2
Theorem 210e9.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι . ∀ x5 x6 . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x0) ⟶ iff (x1 x7) (x2 x7)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x3 x7 = x4 x7) ⟶ 9d1fa.. x0 x1 x3 x5 x6 = 9d1fa.. x0 x2 x4 x5 x6 (proof)
Definition 9d3f2.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (9d1fa.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem da688.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 9d3f2.. (9d1fa.. x0 x1 x2 x3 x4) (proof)
Theorem 9800a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . 9d3f2.. (9d1fa.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem 96b84.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . 9d3f2.. (9d1fa.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 08a4a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 . 9d3f2.. (9d1fa.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem bb961.. : ∀ x0 . 9d3f2.. x0 ⟶ x0 = 9d1fa.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition ac684.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem e41cf.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → ι → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ ac684.. (9d1fa.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 64bec.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 5ef4c.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → ι → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 64bec.. (9d1fa.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Param 1216a.. : ι → (ι → ο) → ι
Definition e6f8c.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ο . λ x3 x4 : ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (d2155.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) (1216a.. x0 x4)))))
Theorem 104bb.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = e6f8c.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem e72e6.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . x0 = f482f.. (e6f8c.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 30c75.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = e6f8c.. x1 x2 x3 x4 x5 ⟶ ∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ x2 x6 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem 1d5e4.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (e6f8c.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Param 2b2e3.. : ι → ι → ι → ο
Known 67416.. : ∀ x0 . ∀ x1 : ι → ι → ο . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ 2b2e3.. (d2155.. x0 x1) x2 x3 = x1 x2 x3
Theorem c6202.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = e6f8c.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 73d5c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = 2b2e3.. (f482f.. (e6f8c.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Param decode_p : ι → ι → ο
Known 931fe.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . prim1 x2 x0 ⟶ decode_p (1216a.. x0 x1) x2 = x1 x2
Theorem 8cbc4.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = e6f8c.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 8f958.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (e6f8c.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 9b43e.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = e6f8c.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 642f0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (e6f8c.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem f7410.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 x8 x9 : ι → ο . e6f8c.. x0 x2 x4 x6 x8 = e6f8c.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10)) (∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10) (proof)
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Known 62ef7.. : ∀ x0 . ∀ x1 x2 : ι → ι → ο . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ iff (x1 x3 x4) (x2 x3 x4)) ⟶ d2155.. x0 x1 = d2155.. x0 x2
Theorem f0c4a.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ο . ∀ x5 x6 x7 x8 : ι → ο . (∀ x9 : ι → ο . (∀ x10 . x9 x10 ⟶ prim1 x10 x0) ⟶ iff (x1 x9) (x2 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x3 x9 x10) (x4 x9 x10)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x5 x9) (x6 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ e6f8c.. x0 x1 x3 x5 x7 = e6f8c.. x0 x2 x4 x6 x8 (proof)
Definition 3030f.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ο . ∀ x5 x6 : ι → ο . x1 (e6f8c.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem d5c55.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . 3030f.. (e6f8c.. x0 x1 x2 x3 x4) (proof)
Theorem 5cc48.. : ∀ x0 . 3030f.. x0 ⟶ x0 = e6f8c.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 4f31d.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 46ace.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 4f31d.. (e6f8c.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 97de1.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 86d05.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 97de1.. (e6f8c.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition a3459.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ο . λ x3 : ι → ο . λ x4 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (d2155.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) x4))))
Theorem 588b8.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = a3459.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem c8bfe.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . x0 = f482f.. (a3459.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 7790e.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = a3459.. x1 x2 x3 x4 x5 ⟶ ∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ x2 x6 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem 88c0b.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (a3459.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 17548.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = a3459.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 96a2a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = 2b2e3.. (f482f.. (a3459.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem ba1ae.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = a3459.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 25e5a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (a3459.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 26708.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = a3459.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem aa92f.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . x4 = f482f.. (a3459.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 89c28.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 : ι → ο . ∀ x8 x9 . a3459.. x0 x2 x4 x6 x8 = a3459.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10)) (x8 = x9) (proof)
Theorem 48143.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ο . ∀ x5 x6 : ι → ο . ∀ x7 . (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ iff (x1 x8) (x2 x8)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ iff (x3 x8 x9) (x4 x8 x9)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ iff (x5 x8) (x6 x8)) ⟶ a3459.. x0 x1 x3 x5 x7 = a3459.. x0 x2 x4 x6 x7 (proof)
Definition db61c.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (a3459.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 4ac71.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ db61c.. (a3459.. x0 x1 x2 x3 x4) (proof)
Theorem fcffe.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . db61c.. (a3459.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 407c2.. : ∀ x0 . db61c.. x0 ⟶ x0 = a3459.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 8f423.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem ba51b.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 8f423.. (a3459.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 2bfcf.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem c8389.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → (ι → ο) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 2bfcf.. (a3459.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition fe7e3.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ο . λ x3 x4 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (d2155.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))
Theorem 4e843.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = fe7e3.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 8411e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 . x0 = f482f.. (fe7e3.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem a7a18.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = fe7e3.. x1 x2 x3 x4 x5 ⟶ ∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ x2 x6 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem 25129.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (fe7e3.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 9f953.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = fe7e3.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 0ad90.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = 2b2e3.. (f482f.. (fe7e3.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 3e984.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = fe7e3.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem a524c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 . x3 = f482f.. (fe7e3.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem ca10d.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = fe7e3.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 171bb.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 . x4 = f482f.. (fe7e3.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 27a4d.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 x8 x9 . fe7e3.. x0 x2 x4 x6 x8 = fe7e3.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (x6 = x7)) (x8 = x9) (proof)
Theorem 74507.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ο . ∀ x5 x6 . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x0) ⟶ iff (x1 x7) (x2 x7)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (x3 x7 x8) (x4 x7 x8)) ⟶ fe7e3.. x0 x1 x3 x5 x6 = fe7e3.. x0 x2 x4 x5 x6 (proof)
Definition 781e8.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ο . ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (fe7e3.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 927ff.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 781e8.. (fe7e3.. x0 x1 x2 x3 x4) (proof)
Theorem 883af.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 . 781e8.. (fe7e3.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 9ac35.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ο . ∀ x3 x4 . 781e8.. (fe7e3.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 1ebb1.. : ∀ x0 . 781e8.. x0 ⟶ x0 = fe7e3.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 0fef8.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem ef0c5.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ι → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 0fef8.. (fe7e3.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition d8a7a.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem e3077.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ο) → ι → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ο . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ d8a7a.. (fe7e3.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)