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Proofgold Signed Transaction

vin
Pr6yb../3b633..
PULPZ../2d409..
vout
Pr6yb../a3aed.. 24.98 bars
TMMxT../36941.. ownership of 51334.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQBf../f9159.. ownership of 9a54b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLKQ../af013.. ownership of cf0a4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW84../b6c1b.. ownership of ed929.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNGT../af4e1.. ownership of b8260.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRD8../17f5d.. ownership of ad5f2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNb7../d46b3.. ownership of fc3fe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb6Q../6b0b3.. ownership of 24120.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFqG../ac11d.. ownership of 5d7d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQiH../1e0bd.. ownership of 73c6a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPWq../4ec5f.. ownership of e9809.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYku../86d56.. ownership of 174f1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMctN../3b658.. ownership of 72750.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUy9../c42e7.. ownership of 1031c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV5y../9b6cb.. ownership of 5e479.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEhx../45a28.. ownership of 8d3c0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHPA../ba753.. ownership of d3f5a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKCt../237d0.. ownership of c4484.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPoV../95226.. ownership of 80085.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTCz../f1a22.. ownership of 6863a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPWt../e3d43.. ownership of 8ab77.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVdd../f28b1.. ownership of a608f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRrZ../b6d43.. ownership of e9aad.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTJk../20099.. ownership of 5a82d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVtJ../ed006.. ownership of 70d81.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMS5w../ef327.. ownership of f9087.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHwd../8bc85.. ownership of 12b50.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdWm../be4ef.. ownership of 73d72.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNi6../164f0.. ownership of e66bf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdbs../dfcc9.. ownership of 4055a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZFU../28ed5.. ownership of 0987d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFBZ../ef906.. ownership of 4a131.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSUL../138ae.. ownership of 69b45.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK1T../67310.. ownership of 94ece.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTuY../512a3.. ownership of 18def.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRak../dcafd.. ownership of 444bb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ8K../00207.. ownership of 9df88.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZgN../93a73.. ownership of 66e69.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYJm../6d3a0.. ownership of fcc31.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPKc../cb743.. ownership of bcaae.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY6d../c1a21.. ownership of 06e33.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdLR../7067e.. ownership of 24d62.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH1L../bd592.. ownership of b2101.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXFp../ad0e6.. ownership of bc9e4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMckL../46905.. ownership of 7ef48.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX23../786c9.. ownership of 3e385.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTta../29e19.. ownership of 6b57f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUgh../9165c.. ownership of 341c1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcZu../dc600.. ownership of 49f62.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP8U../62b8c.. ownership of 3508c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPwh../6917d.. ownership of e86e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZwL../66c64.. ownership of 818c3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb9u../86d8f.. ownership of 0b346.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMag9../6a4ce.. ownership of 834cb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaLr../d90cc.. ownership of 58312.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXHc../4bb5e.. ownership of 89af4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVLJ../58cfe.. ownership of 45095.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVwL../60081.. ownership of 30b3e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEu2../ca10e.. ownership of b869f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRcp../08348.. ownership of 176a3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMT7../c3eaa.. ownership of 773af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWUN../401ec.. ownership of 2f8cc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbCo../663b8.. ownership of cab07.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQyD../ca901.. ownership of a13f3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGHZ../49856.. ownership of a4102.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTz4../327e6.. ownership of 80e2f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZaZ../906bc.. ownership of 65809.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTjK../4a08c.. ownership of 99dd2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNy7../e705e.. ownership of c7fd8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNpU../e7b29.. ownership of a6297.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVb1../cbdcb.. ownership of 63542.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbQj../99570.. ownership of f5f46.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcLV../1a91d.. ownership of 3d8f2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU2j../89604.. ownership of 05e35.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN2r../da7e0.. ownership of 683f8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK71../a3f75.. ownership of 610eb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGvw../bf208.. ownership of 289de.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRCG../0103e.. ownership of 2b189.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKVT../697c9.. ownership of 73744.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK1c../d0ce5.. ownership of e7447.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWzy../55e05.. ownership of 9b86c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaJb../d7ab5.. ownership of 56e2b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW6f../7729b.. ownership of 9ef04.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcQX../baadd.. ownership of f0056.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRxR../481c5.. ownership of caff9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPMj../1fabf.. ownership of 74d95.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU3h../78d5c.. ownership of 98a70.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUC2../64357.. ownership of db903.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKeW../a80c1.. ownership of 8f14c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbro../fbd29.. ownership of f625f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc7X../fc078.. ownership of fc16f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKmk../02ad4.. ownership of 3df02.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP1f../1b089.. ownership of 5acf4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ98../76d9e.. ownership of 81a95.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdVw../44597.. ownership of 1019c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUh7../e15b3.. ownership of 7a7bf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPZX../554b8.. ownership of 91610.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVYb../3afb1.. ownership of 011ac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNZq../5db31.. ownership of 5ec19.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKMd../6dc00.. ownership of b56b0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPxe../b5485.. ownership of 74f86.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRpJ../f7222.. ownership of 9ab42.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJnD../6edc8.. ownership of 91633.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ5H../4faa8.. ownership of 26b43.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQwd../e7808.. ownership of 8bc8a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJw4../ca58e.. ownership of 079a7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaXD../8f8ab.. ownership of 9e504.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMboY../7a4db.. ownership of 33af3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU9x../8f63e.. ownership of 5fe65.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW6M../16036.. ownership of 43949.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK5L../b8be5.. ownership of d2a28.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPxq../92af6.. ownership of c3f6c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb1o../5786f.. ownership of 71580.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZX3../249d4.. ownership of 0274a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN6Z../8bdea.. ownership of 2bf47.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMux../cfdd1.. ownership of 79c0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLbz../4e4ac.. ownership of f9e4c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLyP../42708.. ownership of 44ab4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZD8../c5f50.. ownership of 4222f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKka../3ff2c.. ownership of 9d877.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSc5../068c0.. ownership of 0b40b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbTp../27d45.. ownership of 362e3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa93../d233c.. ownership of 2849e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ3h../7cb1d.. ownership of 56d1b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ2G../30e67.. ownership of f447c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZMC../ec770.. ownership of 84206.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNmx../ab560.. ownership of 5777c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXHW../3b8c8.. ownership of f3e60.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUri../8428a.. ownership of 6901c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdtU../c72ee.. ownership of 651a3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJKk../f2d29.. ownership of 07b63.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMayj../1dcf4.. ownership of f12f7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdSe../1008d.. ownership of 6f8b9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWsi../17299.. ownership of 8feed.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT2Y../236a9.. ownership of 6c751.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP6i../4c98b.. ownership of ecd65.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd9T../fcf88.. ownership of 96ff7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJEX../f7d99.. ownership of 550dd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTGQ../6bc63.. ownership of 13649.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXoh../58585.. ownership of d5d88.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcbN../029f1.. ownership of 97762.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZZ4../474c9.. ownership of 7ee1f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNff../f3966.. ownership of 01947.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNwA../46566.. ownership of 59e7e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMViD../606f3.. ownership of c14f1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSLD../cf258.. ownership of 8b632.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLAq../87ac7.. ownership of 3bcdb.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR3C../1b6a8.. ownership of ca7f1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKg3../1b78e.. ownership of 04077.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTP4../ed44d.. ownership of 08ccc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWZv../79be9.. ownership of 1d1e5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWpF../825f4.. ownership of 6b844.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFde../1bebf.. ownership of 1c0d8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZuk../e3c2f.. ownership of 0090d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMW2../5141b.. ownership of 135b2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXE9../ce4df.. ownership of edef1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXAz../8a9f8.. ownership of d4d11.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRb3../28d27.. ownership of 957ef.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUCo../83a42.. ownership of d976e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPqW../c513a.. ownership of 3fb5d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVXb../b7a17.. ownership of c70b7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcao../64a4c.. ownership of 8942d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJgG../fe13f.. ownership of 3d094.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMeH../91c16.. ownership of 12f0b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPW9../28fa6.. ownership of 38265.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRTZ../b61ae.. ownership of c5bd1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMab4../0726b.. ownership of c596a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaTp../a4789.. ownership of dac2a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHA7../b54b5.. ownership of 373f2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPnC../f4e91.. ownership of ad51e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKrC../ae616.. ownership of 1b748.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMShw../1eb2c.. ownership of 4f82c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdM9../9d0fa.. ownership of a0d6b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYhB../5fc6b.. ownership of 3058d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUbF9../9124e.. 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
Param eb53d.. : ι → CT2 ι
Definition a0d6b.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 : ι → ι . 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (0fc90.. x0 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 97762.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . x0 = a0d6b.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 13649.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . x0 = f482f.. (a0d6b.. 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 96ff7.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . x0 = a0d6b.. 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 6c751.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (a0d6b.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Param e3162.. : ι → ι → ι → ι
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 35054.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ e3162.. (eb53d.. x0 x1) x2 x3 = x1 x2 x3
Theorem 6f8b9.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . x0 = a0d6b.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 07b63.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (a0d6b.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (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
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 6901c.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . x0 = a0d6b.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 5777c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . prim1 x5 x0 ⟶ x3 x5 = f482f.. (f482f.. (a0d6b.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (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 f447c.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . x0 = a0d6b.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 2849e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . x4 = f482f.. (a0d6b.. 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 0b40b.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ι . ∀ x8 x9 . a0d6b.. x0 x2 x4 x6 x8 = a0d6b.. 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)
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 8fdaf.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = x2 x3 x4) ⟶ eb53d.. x0 x1 = eb53d.. 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 4222f.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ι . ∀ x7 . (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ iff (x1 x8) (x2 x8)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x8 x9 = x4 x8 x9) ⟶ (∀ x8 . prim1 x8 x0 ⟶ x5 x8 = x6 x8) ⟶ a0d6b.. x0 x1 x3 x5 x7 = a0d6b.. x0 x2 x4 x6 x7 (proof)
Definition 1b748.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x2 ⟶ prim1 (x5 x6) x2) ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (a0d6b.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem f9e4c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x0 ⟶ prim1 (x3 x4) x0) ⟶ ∀ x4 . prim1 x4 x0 ⟶ 1b748.. (a0d6b.. x0 x1 x2 x3 x4) (proof)
Theorem 2bf47.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . 1b748.. (a0d6b.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 71580.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . 1b748.. (a0d6b.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x3 x5) x0 (proof)
Theorem d2a28.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . 1b748.. (a0d6b.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 5fe65.. : ∀ x0 . 1b748.. x0 ⟶ x0 = a0d6b.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 373f2.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι) → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 9e504.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι . (∀ x9 . prim1 x9 x1 ⟶ x4 x9 = x8 x9) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 373f2.. (a0d6b.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition c596a.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι) → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 8bc8a.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι . (∀ x9 . prim1 x9 x1 ⟶ x4 x9 = x8 x9) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ c596a.. (a0d6b.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition 38265.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 x4 : ι → 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) (d2155.. x0 x4)))))
Theorem 91633.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 38265.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 74f86.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 x5 : ι → ι → ο . x5 x0 (f482f.. (38265.. x0 x1 x2 x3 x4) 4a7ef..) ⟶ x5 (f482f.. (38265.. x0 x1 x2 x3 x4) 4a7ef..) x0 (proof)
Theorem 5ec19.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 38265.. 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 91610.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (38265.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 1019c.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 38265.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 5acf4.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (38265.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (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 fc16f.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 38265.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem 8f14c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (38265.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem 98a70.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 38265.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x5 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 x7 (proof)
Theorem caff9.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x4 x5 x6 = 2b2e3.. (f482f.. (38265.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 x6 (proof)
Theorem 9ef04.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 x8 x9 : ι → ι → ο . 38265.. x0 x2 x4 x6 x8 = 38265.. 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x8 x10 x11 = x9 x10 x11) (proof)
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 9b86c.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 x7 x8 : ι → ι → ο . (∀ x9 : ι → ο . (∀ x10 . x9 x10 ⟶ prim1 x10 x0) ⟶ iff (x1 x9) (x2 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x3 x9 x10 = x4 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x5 x9 x10) (x6 x9 x10)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x7 x9 x10) (x8 x9 x10)) ⟶ 38265.. x0 x1 x3 x5 x7 = 38265.. x0 x2 x4 x6 x8 (proof)
Definition 3d094.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 x6 : ι → ι → ο . x1 (38265.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 73744.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 x4 : ι → ι → ο . 3d094.. (38265.. x0 x1 x2 x3 x4) (proof)
Theorem 289de.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . 3d094.. (38265.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 683f8.. : ∀ x0 . 3d094.. x0 ⟶ x0 = 38265.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition c70b7.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 3d8f2.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ ∀ x9 : ι → ι → ο . (∀ x10 . prim1 x10 x1 ⟶ ∀ x11 . prim1 x11 x1 ⟶ iff (x5 x10 x11) (x9 x10 x11)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ c70b7.. (38265.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition d976e.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 63542.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ ∀ x9 : ι → ι → ο . (∀ x10 . prim1 x10 x1 ⟶ ∀ x11 . prim1 x11 x1 ⟶ iff (x5 x10 x11) (x9 x10 x11)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ d976e.. (38265.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param 1216a.. : ι → (ι → ο) → ι
Definition d4d11.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 : ι → ι → ο . λ 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) (1216a.. x0 x4)))))
Theorem c7fd8.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = d4d11.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 65809.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = f482f.. (d4d11.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem a4102.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = d4d11.. 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 cab07.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (d4d11.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 773af.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = d4d11.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem b869f.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (d4d11.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 45095.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = d4d11.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem 58312.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (d4d11.. x0 x1 x2 x3 x4) (4ae4a.. (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 0b346.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = d4d11.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem e86e6.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (d4d11.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem 49f62.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 : ι → ο . d4d11.. x0 x2 x4 x6 x8 = d4d11.. 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11)) (∀ 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
Theorem 6b57f.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ι → ο . ∀ 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 ⟶ x3 x9 x10 = x4 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x5 x9 x10) (x6 x9 x10)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ d4d11.. x0 x1 x3 x5 x7 = d4d11.. x0 x2 x4 x6 x8 (proof)
Definition 135b2.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 : ι → ι → ο . ∀ x6 : ι → ο . x1 (d4d11.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 7ef48.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 135b2.. (d4d11.. x0 x1 x2 x3 x4) (proof)
Theorem b2101.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 135b2.. (d4d11.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 06e33.. : ∀ x0 . 135b2.. x0 ⟶ x0 = d4d11.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 1c0d8.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem fcc31.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 1c0d8.. (d4d11.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 1d1e5.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 9df88.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 1d1e5.. (d4d11.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 04077.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 : ι → 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) x4))))
Theorem 18def.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 04077.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 69b45.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = f482f.. (04077.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 0987d.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 04077.. 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 e66bf.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (04077.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 12b50.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 04077.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 70d81.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (04077.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem e9aad.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 04077.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem 8ab77.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (04077.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem 80085.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 04077.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem d3f5a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x4 = f482f.. (04077.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 5e479.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 . 04077.. x0 x2 x4 x6 x8 = 04077.. 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11)) (x8 = x9) (proof)
Theorem 72750.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → 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 ⟶ x3 x8 x9 = x4 x8 x9) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ iff (x5 x8 x9) (x6 x8 x9)) ⟶ 04077.. x0 x1 x3 x5 x7 = 04077.. x0 x2 x4 x6 x7 (proof)
Definition 3bcdb.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 : ι → ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (04077.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem e9809.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ 3bcdb.. (04077.. x0 x1 x2 x3 x4) (proof)
Theorem 5d7d8.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . 3bcdb.. (04077.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem fc3fe.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . 3bcdb.. (04077.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem b8260.. : ∀ x0 . 3bcdb.. x0 ⟶ x0 = 04077.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition c14f1.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem cf0a4.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ c14f1.. (04077.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 01947.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 51334.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 01947.. (04077.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)