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Proofgold Signed Transaction

vin
PrKcB../4958c..
PUWwM../93401..
vout
PrKcB../3527c.. 24.98 bars
TMZtz../4c7e5.. ownership of ee478.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWHS../b78d6.. ownership of 793c0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSnu../911e8.. ownership of 931ca.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXF6../aba4b.. ownership of 3a122.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXzS../f5961.. ownership of 58b86.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYnR../507a5.. ownership of 863f3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXap../1adb9.. ownership of a259e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHfR../a64d4.. ownership of bce58.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQHk../d1480.. ownership of b42a7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZbE../f6b07.. ownership of 7b1f8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVPr../ce5b5.. ownership of 66a05.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVVv../f45b5.. ownership of c4bf0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXes../f4614.. ownership of db973.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM66../7af22.. ownership of ce940.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHmo../4693e.. ownership of 379e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVLT../a9bfa.. ownership of cebeb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWRp../03a46.. ownership of abd90.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVKi../ced61.. ownership of db618.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMzq../6c99b.. ownership of 14a76.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV2f../e8611.. ownership of e58b7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPrA../d0226.. ownership of 89916.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTkg../011bf.. ownership of 21d39.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXXv../01203.. ownership of 4fe0c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP6s../e2be3.. ownership of 64ae2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKyS../62217.. ownership of 2c5e3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcHQ../95d06.. ownership of 0924d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQA1../7df66.. ownership of b9f3a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPmE../a6711.. ownership of 48073.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbSv../0b665.. ownership of e6fc5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSHN../cbf93.. ownership of d60d1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQjw../b21c9.. ownership of d9dd8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSKp../72e34.. ownership of c437c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMor../a32a2.. ownership of fd872.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYzD../fcaf3.. ownership of feea9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQsA../d257e.. ownership of 18d49.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMayS../3ce92.. ownership of 9c00f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJRk../6b353.. ownership of c81aa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb4m../15e31.. ownership of af673.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZCZ../007b7.. ownership of bc231.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGqa../c88e6.. ownership of d06c5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH6r../0b6eb.. ownership of 035a3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNow../ed90f.. ownership of bd09f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMGJ../a9338.. ownership of d963b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWEy../021fc.. ownership of c249f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZT5../f151b.. ownership of d45f1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMrL../3a96c.. ownership of bb2bf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX51../5d402.. ownership of c61d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZaE../f7e41.. ownership of 510b8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF4S../6dd6f.. ownership of de947.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGPn../8a8b1.. ownership of eec00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWQ6../a4df0.. ownership of 7e3c3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb9X../2e8a6.. ownership of 61cd2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMeR../04024.. ownership of 39c4e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGpC../2052f.. ownership of 17d14.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVwA../bf065.. ownership of 41cdc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEvN../11492.. ownership of 83e4e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNNF../7c403.. ownership of 1ad09.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNNk../6ed3e.. ownership of 8ac49.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLY9../8c5a3.. ownership of f21b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR29../413f9.. ownership of 4d557.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKM1../8630e.. ownership of 8eb97.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbhp../065b0.. ownership of 0809b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXNd../5ab6c.. ownership of 71dc2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGUX../a0826.. ownership of cc298.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUJP../be63c.. ownership of 67bb9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFTb../9a6cb.. ownership of 415ae.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW5o../e1af6.. ownership of ebcb1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWwv../3d044.. ownership of 33b00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVEY../c922b.. ownership of 72955.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHRd../8f1f5.. ownership of 7d112.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJsS../e1f7a.. ownership of 56472.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFqh../c371b.. ownership of 9b935.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMub../6b38c.. ownership of ef2c1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH1h../4b054.. ownership of 14205.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXrR../32964.. ownership of 86968.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRd4../28165.. ownership of 7f58b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKpk../f75fa.. ownership of e167e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML3w../15e0f.. ownership of a9be8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUdX../e89a6.. ownership of d6ad5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMamH../4552f.. ownership of 27c2d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUap../5d7c1.. ownership of 6e401.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPm5../fb455.. ownership of d000e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLzJ../ad9d2.. ownership of 0e89e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFrT../a3f24.. ownership of 75415.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZXJ../50a7f.. ownership of 2c935.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdQH../b2c7e.. ownership of 745ef.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF28../1e4d8.. ownership of 04c48.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN5c../947e2.. ownership of 94fd5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHuo../bcfc4.. ownership of 339b2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSBA../96d13.. ownership of f5d2f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLQo../812fc.. ownership of be737.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdJB../c591f.. ownership of 01493.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ6z../9f44a.. ownership of ba983.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXhe../b4cfc.. ownership of b50ec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWSv../45fb9.. ownership of 7f895.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV3R../94840.. ownership of 5cb83.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcAF../dffbd.. ownership of 4a94a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ38../63f41.. ownership of 51ae0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU5y../19f93.. ownership of e13f3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMx9../4eaad.. ownership of 9a296.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSzT../abbd8.. ownership of ea1b8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQmY../a57f5.. ownership of 83abf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVTN../d970c.. ownership of f63f1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFkG../40c5c.. ownership of 5c0df.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJrC../36f12.. ownership of 527b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJum../738a4.. ownership of e25b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ3i../d92b2.. ownership of 85c77.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKr4../4d259.. ownership of 746c5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGPG../0b071.. ownership of 25954.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVcu../62452.. ownership of 19767.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFgY../94523.. ownership of a9852.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZXy../2c23b.. ownership of 21849.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQfZ../deb42.. ownership of 02a1c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLd5../836de.. ownership of 1bbcb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEmV../1e275.. ownership of ca5af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPit../9ef2b.. ownership of 70a78.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ9o../3628c.. ownership of 223c0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWok../74f03.. ownership of 0c7e9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLHu../5b3f7.. ownership of 19427.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMMh../243d4.. ownership of 7535d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLRP../99953.. ownership of 51074.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRGf../fd3f6.. ownership of f209b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaX9../1b114.. ownership of 2d21c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJqb../ad367.. ownership of 155fa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTzr../27498.. ownership of 0037b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb9q../ac81e.. ownership of 156ad.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPcE../a9aa6.. ownership of e496c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRed../a18c7.. ownership of 6408c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWTj../4da77.. ownership of 369e2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQGF../7517a.. ownership of cc70c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGBx../2c0e1.. ownership of 540f0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRTq../b5f91.. ownership of 1082a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXtX../cceff.. ownership of a0393.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK9N../492d9.. ownership of b2ff7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPuX../758f7.. ownership of 8ef7a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQQJ../d3f55.. ownership of e4936.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKrj../e9178.. ownership of f200f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFGt../27506.. ownership of 09b21.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPzz../dba79.. ownership of 449e8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV41../c8612.. ownership of d76cb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXkc../37fb0.. ownership of 4cd80.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbzW../30413.. ownership of 35ac3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPp4../7ce7d.. ownership of acf94.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQgg../775b1.. ownership of 3f081.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTHg../5e7e9.. ownership of eb78a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFyj../47e52.. ownership of a896d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX5H../6ec84.. ownership of 07fe2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFtY../5c124.. ownership of 70974.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcG3../f4079.. ownership of 61d02.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVAx../a6206.. ownership of f4861.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ8T../72713.. ownership of 8740e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGEG../d4456.. ownership of ab2a7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYCv../16e9f.. ownership of a8a42.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM8E../b1720.. ownership of 649ad.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZVd../ea90c.. ownership of 2cece.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWEF../c3e97.. ownership of 4ee55.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdQr../e57c1.. ownership of 8fa66.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJcP../77c2d.. ownership of 9cbf7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRxz../89cce.. ownership of f52b0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFPf../49b17.. ownership of 87c36.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd8E../261e5.. ownership of 3db62.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVam../4e676.. ownership of f9428.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRT9../1e0b3.. ownership of 50ab0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTqh../3bf3c.. ownership of ab8be.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQU5../3b2cd.. ownership of 3233e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNtd../cf91c.. ownership of 4755a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbwL../3b5bc.. ownership of 834d5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdxS../13de0.. ownership of a68f5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLxs../3a4de.. ownership of 04214.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVb9../5b7b6.. ownership of 4e021.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaod../e0aaa.. ownership of dd5e6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFDC../af5f9.. ownership of 77cd0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP5s../ae277.. ownership of 28d85.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRaf../54773.. ownership of 1f5c0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcfT../d1eb5.. ownership of d34f8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbEK../41660.. ownership of b623e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN6e../a835a.. ownership of 3f728.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMS2Y../ed7db.. ownership of d2866.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWyT../ac999.. ownership of 59e44.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdcp../99fd0.. ownership of f8b77.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUbA1../6c799.. 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 eb53d.. : ι → CT2 ι
Param 1216a.. : ι → (ι → ο) → ι
Definition 59e44.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ο . λ x3 x4 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (1216a.. 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 07fe2.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 59e44.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem eb78a.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . x0 = f482f.. (59e44.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Param e3162.. : ι → ι → ι → ι
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 35054.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ e3162.. (eb53d.. x0 x1) x2 x3 = x1 x2 x3
Theorem acf94.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 59e44.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 x7 (proof)
Theorem 4cd80.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (59e44.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Param decode_p : ι → ι → ο
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 931fe.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . prim1 x2 x0 ⟶ decode_p (1216a.. x0 x1) x2 = x1 x2
Theorem 449e8.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 59e44.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem f200f.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ x2 x5 = decode_p (f482f.. (59e44.. 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 8ef7a.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 59e44.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem a0393.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . x3 = f482f.. (59e44.. 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 540f0.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 59e44.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 369e2.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . x4 = f482f.. (59e44.. 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 e496c.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . ∀ x6 x7 x8 x9 . 59e44.. x0 x2 x4 x6 x8 = 59e44.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10)) (x6 = x7)) (x8 = x9) (proof)
Param iff : ο → ο → ο
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. 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
Theorem 0037b.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 x6 . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ iff (x3 x7) (x4 x7)) ⟶ 59e44.. x0 x1 x3 x5 x6 = 59e44.. x0 x2 x4 x5 x6 (proof)
Definition 3f728.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (59e44.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 2d21c.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 3f728.. (59e44.. x0 x1 x2 x3 x4) (proof)
Theorem 51074.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . 3f728.. (59e44.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 19427.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . 3f728.. (59e44.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 223c0.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . 3f728.. (59e44.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem ca5af.. : ∀ x0 . 3f728.. x0 ⟶ x0 = 59e44.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition d34f8.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ο) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 02a1c.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ο) → ι → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x3 x8) (x7 x8)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ d34f8.. (59e44.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 28d85.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ο) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem a9852.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ο) → ι → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x3 x8) (x7 x8)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 28d85.. (59e44.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition dd5e6.. := λ x0 . λ x1 x2 : 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..) (0fc90.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) (d2155.. x0 x4)))))
Theorem 25954.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = dd5e6.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 85c77.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 x5 : ι → ι → ο . x5 x0 (f482f.. (dd5e6.. x0 x1 x2 x3 x4) 4a7ef..) ⟶ x5 (f482f.. (dd5e6.. x0 x1 x2 x3 x4) 4a7ef..) x0 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 527b1.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = dd5e6.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x6 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem f63f1.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x1 x5 = f482f.. (f482f.. (dd5e6.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem ea1b8.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = dd5e6.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem e13f3.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (dd5e6.. x0 x1 x2 x3 x4) (4ae4a.. (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 4a94a.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = dd5e6.. 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 7f895.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (dd5e6.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem ba983.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = dd5e6.. 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 be737.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x4 x5 x6 = 2b2e3.. (f482f.. (dd5e6.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 x6 (proof)
Theorem 339b2.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . ∀ x6 x7 x8 x9 : ι → ι → ο . dd5e6.. x0 x2 x4 x6 x8 = dd5e6.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10)) (∀ 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
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Theorem 04c48.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . ∀ x5 x6 x7 x8 : ι → ι → ο . (∀ x9 . prim1 x9 x0 ⟶ x1 x9 = x2 x9) ⟶ (∀ x9 . prim1 x9 x0 ⟶ x3 x9 = x4 x9) ⟶ (∀ 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)) ⟶ dd5e6.. x0 x1 x3 x5 x7 = dd5e6.. x0 x2 x4 x6 x8 (proof)
Definition 04214.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 x6 : ι → ι → ο . x1 (dd5e6.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 2c935.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 x4 : ι → ι → ο . 04214.. (dd5e6.. x0 x1 x2 x3 x4) (proof)
Theorem 0e89e.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . 04214.. (dd5e6.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x5) x0 (proof)
Theorem 6e401.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . 04214.. (dd5e6.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem d6ad5.. : ∀ x0 . 04214.. x0 ⟶ x0 = dd5e6.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 834d5.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem e167e.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 834d5.. (dd5e6.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 3233e.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 86968.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 3233e.. (dd5e6.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 50ab0.. := λ x0 . λ x1 x2 : 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..) (0fc90.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) (1216a.. x0 x4)))))
Theorem ef2c1.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 50ab0.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 56472.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = f482f.. (50ab0.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 72955.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 50ab0.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x6 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem ebcb1.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x1 x5 = f482f.. (f482f.. (50ab0.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 67bb9.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 50ab0.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 71dc2.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (50ab0.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 8eb97.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 50ab0.. 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 f21b1.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (50ab0.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem 1ad09.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 50ab0.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 41cdc.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (50ab0.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem 39c4e.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 : ι → ο . 50ab0.. x0 x2 x4 x6 x8 = 50ab0.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10) (proof)
Theorem 7e3c3.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . ∀ x5 x6 : ι → ι → ο . ∀ x7 x8 : ι → ο . (∀ x9 . prim1 x9 x0 ⟶ x1 x9 = x2 x9) ⟶ (∀ x9 . prim1 x9 x0 ⟶ x3 x9 = x4 x9) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x5 x9 x10) (x6 x9 x10)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ 50ab0.. x0 x1 x3 x5 x7 = 50ab0.. x0 x2 x4 x6 x8 (proof)
Definition 3db62.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ι → ο . ∀ x6 : ι → ο . x1 (50ab0.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem de947.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 3db62.. (50ab0.. x0 x1 x2 x3 x4) (proof)
Theorem c61d8.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 3db62.. (50ab0.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x5) x0 (proof)
Theorem d45f1.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 3db62.. (50ab0.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem d963b.. : ∀ x0 . 3db62.. x0 ⟶ x0 = 50ab0.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition f52b0.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 035a3.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . (∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ f52b0.. (50ab0.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 8fa66.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem bc231.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . (∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 8fa66.. (50ab0.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 2cece.. := λ x0 . λ x1 x2 : 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..) (0fc90.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) x4))))
Theorem c81aa.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 2cece.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 18d49.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = f482f.. (2cece.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem fd872.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 2cece.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x6 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 (proof)
Theorem d9dd8.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x1 x5 = f482f.. (f482f.. (2cece.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem e6fc5.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 2cece.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem b9f3a.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (2cece.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 2c5e3.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 2cece.. 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 4fe0c.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (2cece.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem 89916.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 2cece.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 14a76.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x4 = f482f.. (2cece.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem abd90.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 . 2cece.. x0 x2 x4 x6 x8 = 2cece.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11)) (x8 = x9) (proof)
Theorem 379e6.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . ∀ x5 x6 : ι → ι → ο . ∀ x7 . (∀ x8 . prim1 x8 x0 ⟶ x1 x8 = x2 x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ x3 x8 = x4 x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ iff (x5 x8 x9) (x6 x8 x9)) ⟶ 2cece.. x0 x1 x3 x5 x7 = 2cece.. x0 x2 x4 x6 x7 (proof)
Definition a8a42.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (2cece.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem db973.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ a8a42.. (2cece.. x0 x1 x2 x3 x4) (proof)
Theorem 66a05.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . a8a42.. (2cece.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x5) x0 (proof)
Theorem b42a7.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . a8a42.. (2cece.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem a259e.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . a8a42.. (2cece.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 58b86.. : ∀ x0 . a8a42.. x0 ⟶ x0 = 2cece.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 8740e.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 931ca.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ι → ι . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . (∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 8740e.. (2cece.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 61d02.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem ee478.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ι → ο . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . (∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x2 x7 = x6 x7) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 61d02.. (2cece.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)