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Proofgold Signed Transaction

vin
PrLJq../4cccb..
PURtZ../7801d..
vout
PrLJq../c1f91.. 19.99 bars
TMPQt../41960.. ownership of 3b05e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQNJ../48104.. ownership of 07254.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TML6U../26ee3.. ownership of 635d1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQYH../204e2.. ownership of 2cd70.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQb3../fbdf5.. ownership of 2967c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMEh9../86fc6.. ownership of 927a7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLtN../d7e29.. ownership of 4e4ad.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSJA../cd4f6.. ownership of a7f0b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUjG../dd086.. ownership of ecc62.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLLG../7ad50.. ownership of ee5c4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMV9S../27bd8.. ownership of fee39.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbFu../1bb42.. ownership of df432.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHzZ../acb3c.. ownership of 6feb4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMEhi../cac68.. ownership of d4326.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTUo../81a2d.. ownership of 3f154.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbuH../d7db8.. ownership of 47bb3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMd3Z../0981a.. ownership of 42dda.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMT9B../1f073.. ownership of 491bb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSea../c4d78.. ownership of d4ea6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLVB../d6c75.. ownership of 5ea68.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSz3../cb0fa.. ownership of e31f7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTR2../ff36b.. ownership of 323d1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRDh../46239.. ownership of a3c76.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRwk../bda01.. ownership of fed6c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMP1A../6e7de.. ownership of 6603f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQyu../90862.. ownership of 22917.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSdP../2707c.. ownership of 79ecf.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHbP../72f22.. ownership of b0f82.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRW9../15ba9.. ownership of 7e005.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdQk../da0e7.. ownership of fc5df.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHhz../2ef3d.. ownership of 05f1b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZfj../f5950.. ownership of 31956.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYx7../f333f.. ownership of 6e387.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMEi9../80a6b.. ownership of 9a2b1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMK6L../f319d.. ownership of 0a36d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWDs../a36c1.. ownership of 5200f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWUw../4c58d.. ownership of c2bb8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMR6d../3b610.. ownership of dc5af.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPaD../dae38.. ownership of 7ffab.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKzu../7c748.. ownership of ce59d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcRA../ee670.. ownership of 88d1a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUW6../48829.. ownership of 4fe62.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYYq../d01dc.. ownership of 7e2a5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVUu../f58b4.. ownership of f7749.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZeQ../39ffe.. ownership of 27ade.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPDw../9b279.. ownership of 0d3ca.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMde2../25c01.. ownership of 480cd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVVd../b0e41.. ownership of bf091.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUu4../62bf3.. ownership of 7abf4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVxa../27b76.. ownership of b6909.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFvh../9f722.. ownership of 2a06f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZ94../baeab.. ownership of f3b61.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLCy../70ad8.. ownership of 5b4ed.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXZH../fad4d.. ownership of aa5c7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFg3../bfeba.. ownership of b50a5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXxt../e05ac.. ownership of 3a20a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLnF../5ffb7.. ownership of 667ed.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXd8../ad1cc.. ownership of e872f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXwr../dbb17.. ownership of 84361.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRgF../6f5ed.. ownership of 61069.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJTZ../f3a0d.. ownership of 0c2e8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXmf../bfd8d.. ownership of 443af.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPMX../326cb.. ownership of 302f9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXXZ../18ba2.. ownership of 42196.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPNM../5af3b.. ownership of 76f24.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUE3../e8ed9.. ownership of 148c7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcV6../ba559.. ownership of cdbe1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaLy../ac5be.. ownership of a502e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVqy../8a280.. ownership of 985a2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPM5../4ad22.. ownership of baabb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLtL../80fdb.. ownership of 89267.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRQ8../91afc.. ownership of 88ed0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaMJ../9c1fd.. ownership of 33405.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGth../7c6d4.. ownership of 55bd3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMU6T../905f7.. ownership of 70f8f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRbk../c3fd4.. ownership of 89c32.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbmo../014e2.. ownership of e5cbd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMBA../7f984.. ownership of f927f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFYo../f229f.. ownership of 7de3c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMFb../77572.. ownership of abde0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbSV../35fea.. ownership of 20213.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMR2u../04c8a.. ownership of ec7e3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMX4c../41aef.. ownership of 0943f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRr9../6b7af.. ownership of b1ee8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKij../d4d5c.. ownership of 223a4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaf4../76611.. ownership of e22c9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcii../1c69b.. ownership of 642df.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTEz../a8875.. ownership of f5c01.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXEe../b37cf.. ownership of 3f9d5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGKF../34303.. ownership of 201c0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXUT../12dcf.. ownership of c19c9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZFM../aa6db.. ownership of 99cae.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaSm../28a0c.. ownership of 702f9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHBU../fbac3.. ownership of 67125.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMacs../68ff9.. ownership of e7b29.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKas../37841.. ownership of 9be85.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUxm../eea7f.. ownership of bbed6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWWA../7d6b0.. ownership of 44dc6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTB9../0a6e4.. ownership of aa6ea.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJW2../194af.. ownership of cd5b1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMciu../1c5ad.. ownership of c4dc9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZCA../62ff2.. ownership of 597bf.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZHV../c2345.. ownership of 4110f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPkv../eb803.. ownership of 60f68.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQw4../f9877.. ownership of 2ac51.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXEP../cf7d7.. ownership of 0f869.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVgV../9b249.. ownership of 0bb39.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZKT../825cf.. ownership of 6b3ec.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMH4z../e0075.. ownership of bd041.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKHs../a4cb4.. ownership of a3678.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFvu../84540.. ownership of 866ca.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVZt../04975.. ownership of 3f466.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZRh../f1cd9.. ownership of 292e8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcBK../79f0f.. ownership of 7150e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXaV../d078b.. ownership of 12451.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaSt../b4eef.. ownership of c2a5c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMP57../32a0b.. ownership of faf62.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSer../df29c.. ownership of 1e75c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMarr../b437d.. ownership of 9c9f4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVhT../39117.. ownership of 8fcfb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWUL../ff271.. ownership of 1bd93.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFqd../2fef6.. ownership of 325bc.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMThv../d1459.. ownership of 0bf39.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTGX../aceea.. ownership of 775ad.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMc6U../32c72.. ownership of f1f07.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaa6../a7e84.. ownership of ba194.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTRW../14ddf.. ownership of f8286.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPHE../cbf46.. ownership of 15d07.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJ8A../5bb45.. ownership of ad938.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHH3../99082.. ownership of e1f75.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPiT../cc4ae.. ownership of cff9f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbeK../88de7.. ownership of 3917d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TML49../7ef19.. ownership of b91ee.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQg5../78676.. ownership of 90c32.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdT2../62213.. ownership of 02d3f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSK5../d35ab.. ownership of c0d4b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZL8../b72c1.. ownership of e4f10.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMKW../33257.. ownership of 01152.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMjE../1efec.. ownership of d484b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVaA../e002c.. ownership of 401ae.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWE8../a8f91.. ownership of 0cbd8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMX6U../ec107.. ownership of a82a6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXsf../bde5e.. ownership of abad8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTfr../bda66.. ownership of 3795c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNTi../1335f.. ownership of 63f04.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMUp../9cd98.. ownership of dd5c8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMG9R../4338b.. ownership of 54060.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFCP../ecbdd.. ownership of 49a26.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVVz../a9c63.. ownership of f3f77.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYLZ../5cf4c.. ownership of f1bf0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbUR../0cf67.. ownership of 7bf04.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPWh../e6650.. ownership of 5fb65.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKrK../efea4.. ownership of 0a774.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPL8../6bd90.. ownership of 1363a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXmq../498ed.. ownership of a698e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFy5../e97ac.. ownership of 64706.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYPf../76763.. ownership of edc55.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMN1A../93330.. ownership of f9eb4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRCZ../885c4.. ownership of 53a20.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKSw../9f8c9.. ownership of 7f8cf.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbu2../334dc.. ownership of dcdae.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSaB../b3f8d.. ownership of d26df.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZRF../b97b4.. ownership of 80022.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMEi6../f4c75.. ownership of c1cf0.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSn2../a8be1.. ownership of 69fc9.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPgJ../a1ba4.. ownership of 0bec4.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXew../bb251.. ownership of 896af.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVFC../ace1a.. ownership of 4db3f.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXhE../f6584.. ownership of 0fd05.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTQr../26e6a.. ownership of cbc96.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYkm../a459a.. ownership of cd21d.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKvh../eafec.. ownership of 4a3ad.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXkF../0d35b.. ownership of 27f38.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQco../80455.. ownership of 70547.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMLm../e9877.. ownership of c990c.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTWJ../d5866.. ownership of f71ce.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaK5../69db5.. ownership of 48567.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJXB../497c4.. ownership of 720f7.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZo8../540cc.. ownership of 8b59f.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNCX../9f703.. ownership of eb51e.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPHB../84d35.. ownership of e535d.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLVr../97c3e.. ownership of dbc8e.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNCQ../3c0cd.. ownership of 0040b.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNgN../95fca.. ownership of 61320.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRZ2../ef0ae.. ownership of 1670d.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSTD../9a415.. ownership of 424e0.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJJP../e7be2.. ownership of b0c30.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKff../2fe96.. ownership of 090b8.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcVK../dbdac.. ownership of cfc82.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
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PUe31../59be2.. 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
Definition e707a.. := λ x0 . λ x1 x2 : ι → ι → ι . λ x3 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) x3)))
Param f482f.. : ι → ι → ι
Known 9f6be.. : ∀ x0 x1 x2 x3 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) x1 (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)))) 4a7ef.. = x0
Theorem dcdae.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 . x0 = e707a.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 53a20.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . x0 = f482f.. (e707a.. x0 x1 x2 x3) 4a7ef.. (proof)
Param e3162.. : ι → ι → ι → ι
Known 8a328.. : ∀ x0 x1 x2 x3 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) x1 (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)))) (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 edc55.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 . x0 = e707a.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem a698e.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (e707a.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (proof)
Known 142e6.. : ∀ x0 x1 x2 x3 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) x1 (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)))) (4ae4a.. (4ae4a.. 4a7ef..)) = x2
Theorem 0a774.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 . x0 = e707a.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 7bf04.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = e3162.. (f482f.. (e707a.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Known 62a6b.. : ∀ x0 x1 x2 x3 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) x1 (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 x3)))) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x3
Theorem f3f77.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 . x0 = e707a.. x1 x2 x3 x4 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 54060.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . x3 = f482f.. (e707a.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Definition and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known and4I : ∀ x0 x1 x2 x3 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ and (and (and x0 x1) x2) x3
Theorem 63f04.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι → ι . ∀ x6 x7 . e707a.. x0 x2 x4 x6 = e707a.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9)) (x6 = x7) (proof)
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 abad8.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι → ι . ∀ x5 . (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x1 x6 x7 = x2 x6 x7) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x3 x6 x7 = x4 x6 x7) ⟶ e707a.. x0 x1 x3 x5 = e707a.. x0 x2 x4 x5 (proof)
Definition 06179.. := 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 → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 . prim1 x5 x2 ⟶ x1 (e707a.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 0cbd8.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 . prim1 x3 x0 ⟶ 06179.. (e707a.. x0 x1 x2 x3) (proof)
Theorem d484b.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . 06179.. (e707a.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem e4f10.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . 06179.. (e707a.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x4 x5) x0 (proof)
Theorem 02d3f.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . 06179.. (e707a.. x0 x1 x2 x3) ⟶ prim1 x3 x0 (proof)
Theorem b91ee.. : ∀ x0 . 06179.. x0 ⟶ x0 = e707a.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 677e4.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem cff9f.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 677e4.. (e707a.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 2f4b2.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem ad938.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ο . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 2f4b2.. (e707a.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition d89a7.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι . λ x3 : ι → ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (d2155.. x0 x3))))
Theorem f8286.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = d89a7.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem f1f07.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . x4 x0 (f482f.. (d89a7.. x0 x1 x2 x3) 4a7ef..) ⟶ x4 (f482f.. (d89a7.. x0 x1 x2 x3) 4a7ef..) x0 (proof)
Theorem 0bf39.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = d89a7.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 1bd93.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (d89a7.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 9c9f4.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = d89a7.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem faf62.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x2 x4 = f482f.. (f482f.. (d89a7.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (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 12451.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = d89a7.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x5 x6 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem 292e8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x3 x4 x5 = 2b2e3.. (f482f.. (d89a7.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 x5 (proof)
Theorem 866ca.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . d89a7.. x0 x2 x4 x6 = d89a7.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x6 x8 x9 = x7 x8 x9) (proof)
Param iff : ο → ο → ο
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 bd041.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι . ∀ x5 x6 : ι → ι → ο . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x3 x7 = x4 x7) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (x5 x7 x8) (x6 x7 x8)) ⟶ d89a7.. x0 x1 x3 x5 = d89a7.. x0 x2 x4 x6 (proof)
Definition 809f6.. := 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 → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ι → ο . x1 (d89a7.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 0bb39.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ι → ο . 809f6.. (d89a7.. x0 x1 x2 x3) (proof)
Theorem 2ac51.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . 809f6.. (d89a7.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem 4110f.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . 809f6.. (d89a7.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem c4dc9.. : ∀ x0 . 809f6.. x0 ⟶ x0 = d89a7.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition cfc82.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem aa6ea.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x4 x8 x9) (x7 x8 x9)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ cfc82.. (d89a7.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition b0c30.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem bbed6.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x4 x8 x9) (x7 x8 x9)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ b0c30.. (d89a7.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Param 1216a.. : ι → (ι → ο) → ι
Definition 1670d.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι . λ x3 : ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (1216a.. x0 x3))))
Theorem e7b29.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . x0 = 1670d.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 702f9.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ο . x0 = f482f.. (1670d.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem c19c9.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . x0 = 1670d.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 3f9d5.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (1670d.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem 642df.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . x0 = 1670d.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 223a4.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x2 x4 = f482f.. (f482f.. (1670d.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (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 0943f.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . x0 = 1670d.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x4 x5 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 20213.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x3 x4 = decode_p (f482f.. (1670d.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (proof)
Theorem 7de3c.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι . ∀ x6 x7 : ι → ο . 1670d.. x0 x2 x4 x6 = 1670d.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8)) (∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8) (proof)
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Theorem e5cbd.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι . ∀ x5 x6 : ι → ο . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x3 x7 = x4 x7) ⟶ (∀ x7 . prim1 x7 x0 ⟶ iff (x5 x7) (x6 x7)) ⟶ 1670d.. x0 x1 x3 x5 = 1670d.. x0 x2 x4 x6 (proof)
Definition 0040b.. := 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 → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ο . x1 (1670d.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 70f8f.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ο . 0040b.. (1670d.. x0 x1 x2 x3) (proof)
Theorem 33405.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ο . 0040b.. (1670d.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem 89267.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 : ι → ο . 0040b.. (1670d.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 (proof)
Theorem 985a2.. : ∀ x0 . 0040b.. x0 ⟶ x0 = 1670d.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition e535d.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem cdbe1.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → (ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ e535d.. (1670d.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 8b59f.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 76f24.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → (ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ 8b59f.. (1670d.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 48567.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι . λ x3 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) x3)))
Theorem 302f9.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . x0 = 48567.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 0c2e8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . x0 = f482f.. (48567.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem 84361.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . x0 = 48567.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 667ed.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (48567.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem b50a5.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . x0 = 48567.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 5b4ed.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ x2 x4 = f482f.. (f482f.. (48567.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 2a06f.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . x0 = 48567.. x1 x2 x3 x4 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 7abf4.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . x3 = f482f.. (48567.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 480cd.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι . ∀ x6 x7 . 48567.. x0 x2 x4 x6 = 48567.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8)) (x6 = x7) (proof)
Theorem 27ade.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι . ∀ x5 . (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x1 x6 x7 = x2 x6 x7) ⟶ (∀ x6 . prim1 x6 x0 ⟶ x3 x6 = x4 x6) ⟶ 48567.. x0 x1 x3 x5 = 48567.. x0 x2 x4 x5 (proof)
Definition c990c.. := 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 → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 . prim1 x5 x2 ⟶ x1 (48567.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 7e2a5.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 . prim1 x3 x0 ⟶ c990c.. (48567.. x0 x1 x2 x3) (proof)
Theorem 88d1a.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . c990c.. (48567.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem 7ffab.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . c990c.. (48567.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 (proof)
Theorem c2bb8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . c990c.. (48567.. x0 x1 x2 x3) ⟶ prim1 x3 x0 (proof)
Theorem 0a36d.. : ∀ x0 . c990c.. x0 ⟶ x0 = 48567.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 27f38.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 6e387.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 27f38.. (48567.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition cd21d.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 05f1b.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ cd21d.. (48567.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 0fd05.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι → ο . λ x3 : ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (d2155.. x0 x2) (1216a.. x0 x3))))
Theorem 7e005.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = 0fd05.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 79ecf.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . x0 = f482f.. (0fd05.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem 6603f.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = 0fd05.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem a3c76.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (0fd05.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem e31f7.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = 0fd05.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem d4ea6.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = 2b2e3.. (f482f.. (0fd05.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Theorem 42dda.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = 0fd05.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x4 x5 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 3f154.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x3 x4 = decode_p (f482f.. (0fd05.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (proof)
Theorem 6feb4.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 : ι → ο . 0fd05.. x0 x2 x4 x6 = 0fd05.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x2 x8 x9 = x3 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8) (proof)
Theorem fee39.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 x6 : ι → ο . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (x3 x7 x8) (x4 x7 x8)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ iff (x5 x7) (x6 x7)) ⟶ 0fd05.. x0 x1 x3 x5 = 0fd05.. x0 x2 x4 x6 (proof)
Definition 896af.. := 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 → ι → ο . ∀ x5 : ι → ο . x1 (0fd05.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem ecc62.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . 896af.. (0fd05.. x0 x1 x2 x3) (proof)
Theorem 4e4ad.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . 896af.. (0fd05.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem 2967c.. : ∀ x0 . 896af.. x0 ⟶ x0 = 0fd05.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 69fc9.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 635d1.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι → ο . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ iff (x3 x7 x8) (x6 x7 x8)) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ 69fc9.. (0fd05.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 80022.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 3b05e.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ι → ο . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ iff (x3 x7 x8) (x6 x7 x8)) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ 80022.. (0fd05.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)