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Proofgold Signed Transaction

vin
Pr9kG../45b3e..
PUeTk../702a5..
vout
Pr9kG../dc281.. 24.98 bars
TMT8X../a0cf7.. ownership of 61142.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUSs../904cf.. ownership of 1b419.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFVU../5ea50.. ownership of ffddd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFxR../58f59.. ownership of 7d9c8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcS8../fa338.. ownership of 290eb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMU1../b1d27.. ownership of 64bf3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbov../7d236.. ownership of 14447.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdLf../1fb1d.. ownership of ba442.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbgU../6a652.. ownership of fedac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbU3../e6f20.. ownership of 06574.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVnG../1a5a6.. ownership of 10c49.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbRk../7b58d.. ownership of 1062c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRZF../d65c1.. ownership of 5c4b8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZio../7687c.. ownership of 5f4fa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcaU../73aa3.. ownership of 0dcb9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMyX../04a80.. ownership of 8f3a9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJZT../2ea34.. ownership of 5cc8d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWCc../26f00.. ownership of 3df25.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFei../14d4e.. ownership of 8c421.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHY1../321a7.. ownership of afe42.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLwQ../93824.. ownership of c4fb2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWNm../9278d.. ownership of 40b61.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPnU../5f47f.. ownership of eaad1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTe1../4e5f0.. ownership of 37557.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQYi../19df9.. ownership of 5da7d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRya../3242e.. ownership of c6f7a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUxN../c198b.. ownership of bf883.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRn6../bfd7d.. ownership of f0603.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNhK../460dc.. ownership of d6c77.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ8Z../3c7ca.. ownership of 19c36.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLeZ../1f103.. ownership of 22e75.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbcZ../b953f.. ownership of fc264.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWpm../ad8b2.. ownership of f6f08.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYSH../d4802.. ownership of b0365.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT3A../58818.. ownership of 2ab54.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTki../65e9b.. ownership of 99629.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbzN../5ca91.. ownership of 063b4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMFA../4ede7.. ownership of e0bc0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcrK../aea93.. ownership of 25c57.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMr1../5e0a5.. ownership of e0c9d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLzN../852da.. ownership of 2f766.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ6c../bdae0.. ownership of c2784.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb5f../f7aa2.. ownership of 4c198.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSNk../8d2b5.. ownership of 3d8b6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHj2../caae3.. ownership of 3a31c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcAz../d3e59.. ownership of c96df.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPuA../924f5.. ownership of 08be0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMamW../3567c.. ownership of 90584.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdco../4ae0f.. ownership of 68c0b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWS3../4db51.. ownership of 3ca00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM9h../7352e.. ownership of 36098.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPyK../77443.. ownership of ab05d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdbd../0ae92.. ownership of 0a9b2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFMb../e12eb.. ownership of 4fcf1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ6R../ad6c1.. ownership of 4a788.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHdh../057ec.. ownership of ab18f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQXD../e53fc.. ownership of 35d4e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV89../aa0c9.. ownership of c26ef.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUbe../80597.. ownership of 5aadd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU1Z../043b9.. ownership of ecbc0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGHM../4e05b.. ownership of db2c8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKQF../bb5eb.. ownership of 42965.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPPj../d3a5a.. ownership of f1a5f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSFT../e8839.. ownership of 62860.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKUo../3b1ef.. ownership of 05f51.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdvm../67894.. ownership of 1800b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM21../fbe9c.. ownership of d43b4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFW1../f5039.. ownership of 92a66.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGk8../93ec4.. ownership of 05c42.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUtd../10277.. ownership of 9b67c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV1j../1beac.. ownership of 9fd74.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQmZ../6e688.. ownership of a6b18.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKMH../2f5e8.. ownership of 95ea3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSdR../8597e.. ownership of 8ea69.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP43../265e1.. ownership of 223ee.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGPk../b987e.. ownership of df78b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLip../ba184.. ownership of 223da.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHWx../eb227.. ownership of 0e805.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVpB../5ca1d.. ownership of bcc0c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQQV../1f21e.. ownership of 6078e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbMg../6a346.. ownership of b1824.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLM8../12e24.. ownership of 4bfd6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU7h../07573.. ownership of 9e42b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFPT../c4d55.. ownership of 8d6a4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHbr../39ccc.. ownership of 03cda.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNKD../f0c07.. ownership of 4cd0c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd99../33942.. ownership of 2092e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVSn../ccc96.. ownership of 60daf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJgo../c4dbe.. ownership of babf6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbG4../94492.. ownership of 17081.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMPG../0ace2.. ownership of abda6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMkS../d2511.. ownership of 7b2a2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJoB../ea1d5.. ownership of 365e9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN1j../2beb2.. ownership of 73e63.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPyh../e12ab.. ownership of 9dfac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ2N../28eb6.. ownership of ea777.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSuF../c25a0.. ownership of ff25b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLfT../00aba.. ownership of cc631.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc5S../fc32c.. ownership of 98709.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNow../c9602.. ownership of 45c36.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRN9../fec7e.. ownership of 5508b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNwY../3fdd4.. ownership of 4af70.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdUS../59160.. ownership of 1c20d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKzp../6dc49.. ownership of f4cef.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdFu../6e28a.. ownership of 2bb37.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGHZ../4d311.. ownership of 6dd8f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJzr../a720c.. ownership of 48f4e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNP2../97fd9.. ownership of 5f8c8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQGt../b1d4b.. ownership of 10c2e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWjG../bf9eb.. ownership of 93ad6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLn9../86d2f.. ownership of d6a83.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNMf../e4c91.. ownership of e6322.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHqY../b832f.. ownership of 48ea9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWq2../b0a5b.. ownership of 08293.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGYo../dcce0.. ownership of f5284.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLuC../0613c.. ownership of 71606.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHPQ../33048.. ownership of 48205.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWS9../4a2aa.. ownership of 943b8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXmD../bbd99.. ownership of fba5f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRCc../f46b7.. ownership of 4e925.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbBN../072f8.. ownership of f08de.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGKv../3c601.. ownership of 44c19.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUBe../acf4e.. ownership of 270c1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGVq../993f3.. ownership of df484.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPRg../3c0f0.. ownership of 7d48e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXqY../4092b.. ownership of fa28a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHqY../62f0f.. ownership of ce3ec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ7u../76bc3.. ownership of fbb84.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbGX../5015b.. ownership of 01f39.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ9d../dbe88.. ownership of beb76.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMBJ../a796a.. ownership of e176b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ6A../f0d08.. ownership of b39ff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK8B../603c9.. ownership of 84335.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVqx../552c4.. ownership of 12482.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGQR../8aa59.. ownership of 36f32.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWxu../df3ef.. ownership of 9c466.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPbi../9c36e.. ownership of 25edf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLe7../3b18e.. ownership of f6965.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTV3../56fb8.. ownership of 99347.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMafD../0001c.. ownership of 19aa5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJNb../59eb3.. ownership of 19106.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLME../002ae.. ownership of 70e7c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZR3../94420.. ownership of 16264.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWYL../ca5df.. ownership of f44cc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXnM../c5a01.. ownership of aa1f5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYEy../abe39.. ownership of 942aa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdgn../97642.. ownership of 54425.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY3U../c94d3.. ownership of 51d0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVHN../1e419.. ownership of b1f5f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQDB../14cd1.. ownership of 4446d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHKY../d3603.. ownership of 9833d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRjM../22b7f.. ownership of fa060.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPFa../050d0.. ownership of 0499f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZVv../fec0a.. ownership of 8fd00.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHK7../88d44.. ownership of 9ad8d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGFC../9e745.. ownership of 181a8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcqR../ec943.. ownership of 7c481.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTDy../1c9af.. ownership of 9401d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUuK../9c675.. ownership of 94613.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQNx../9eb9b.. ownership of dcc61.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcvW../aff7f.. ownership of 83aaa.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHyT../f84b0.. ownership of 286fa.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbK9../3c2c8.. ownership of a5367.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYjd../ba391.. ownership of 59c00.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHpp../7e4d2.. ownership of 4e60e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRfh../a0221.. ownership of 159f0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWzD../a3fe0.. ownership of 1eafe.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ2Q../aa750.. ownership of 59f7b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJHP../8d7ae.. ownership of 8c11b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUUV../12d7d.. ownership of 5597d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKtT../3f24a.. ownership of 8695a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWxE../142fe.. ownership of 710dd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXky../ec9e9.. ownership of 38635.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVUK../e9c40.. ownership of a5ee3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGiv../e1947.. ownership of 39199.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTJq../8c744.. ownership of 4dae9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW8P../b2959.. ownership of 4aeb5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG8X../20310.. ownership of c0998.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZgf../e11ff.. ownership of 8ac7d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGzD../eb8ae.. ownership of db473.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbkg../d7acc.. ownership of 56056.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTuo../956a8.. ownership of a753f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaKd../d4cf1.. ownership of 98165.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLDz../2fa63.. ownership of fa70a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUZMA../a1b0e.. 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 1216a.. : ι → (ι → ο) → ι
Definition 98165.. := λ x0 . λ x1 : (ι → ο) → ο . 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..) (e0e40.. 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 9833d.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 98165.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem b1f5f.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 . x0 = f482f.. (98165.. 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 54425.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 98165.. 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 aa1f5.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (98165.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (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 16264.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 98165.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 19106.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ x2 x5 = decode_p (f482f.. (98165.. 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 99347.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 98165.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 25edf.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 . x3 = f482f.. (98165.. 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 36f32.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . x0 = 98165.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 84335.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 . x4 = f482f.. (98165.. 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 e176b.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ο . ∀ x6 x7 x8 x9 . 98165.. x0 x2 x4 x6 x8 = 98165.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 : ι → ο . (∀ x11 . x10 x11 ⟶ prim1 x11 x0) ⟶ x2 x10 = x3 x10)) (∀ x10 . prim1 x10 x0 ⟶ x4 x10 = x5 x10)) (x6 = x7)) (x8 = x9) (proof)
Param iff : ο → ο → ο
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. 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 01f39.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ο . ∀ x5 x6 . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x0) ⟶ iff (x1 x7) (x2 x7)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ iff (x3 x7) (x4 x7)) ⟶ 98165.. x0 x1 x3 x5 x6 = 98165.. x0 x2 x4 x5 x6 (proof)
Definition 56056.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (98165.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem ce3ec.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 56056.. (98165.. x0 x1 x2 x3 x4) (proof)
Theorem 7d48e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 . 56056.. (98165.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 270c1.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . ∀ x3 x4 . 56056.. (98165.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem f08de.. : ∀ x0 . 56056.. x0 ⟶ x0 = 98165.. (f482f.. x0 4a7ef..) (decode_c (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 8ac7d.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ο) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (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 fba5f.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ο) → ι → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x3 x8) (x7 x8)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 8ac7d.. (98165.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 4aeb5.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ο) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (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 48205.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ο) → ι → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ο . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x3 x8) (x7 x8)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 4aeb5.. (98165.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param eb53d.. : ι → CT2 ι
Definition 39199.. := λ x0 . λ x1 x2 x3 : ι → ι → ι . λ x4 : ι → ι . 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (eb53d.. x0 x3) (0fc90.. x0 x4)))))
Theorem f5284.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . x0 = 39199.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 48ea9.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . x0 = f482f.. (39199.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Param e3162.. : ι → ι → ι → ι
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 d6a83.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . x0 = 39199.. 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 10c2e.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (39199.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 48f4e.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . x0 = 39199.. 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 2bb37.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (39199.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 1c20d.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . x0 = 39199.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem 5508b.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = e3162.. (f482f.. (39199.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 98709.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . x0 = 39199.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem ff25b.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = f482f.. (f482f.. (39199.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem 9dfac.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 x6 x7 : ι → ι → ι . ∀ x8 x9 : ι → ι . 39199.. x0 x2 x4 x6 x8 = 39199.. 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 ⟶ ∀ 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 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
Theorem 365e9.. : ∀ x0 . ∀ x1 x2 x3 x4 x5 x6 : ι → ι → ι . ∀ x7 x8 : ι → ι . (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x1 x9 x10 = x2 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x3 x9 x10 = x4 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x5 x9 x10 = x6 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ x7 x9 = x8 x9) ⟶ 39199.. x0 x1 x3 x5 x7 = 39199.. x0 x2 x4 x6 x8 (proof)
Definition 38635.. := 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 : ι → ι → ι . (∀ x6 . prim1 x6 x2 ⟶ ∀ x7 . prim1 x7 x2 ⟶ prim1 (x5 x6 x7) x2) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x2 ⟶ prim1 (x6 x7) x2) ⟶ x1 (39199.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem abda6.. : ∀ 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 : ι → ι → ι . (∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x3 x4 x5) x0) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x0 ⟶ prim1 (x4 x5) x0) ⟶ 38635.. (39199.. x0 x1 x2 x3 x4) (proof)
Theorem babf6.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . 38635.. (39199.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 2092e.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . 38635.. (39199.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 03cda.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . 38635.. (39199.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x3 x5 x6) x0 (proof)
Theorem 9e42b.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι . 38635.. (39199.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x4 x5) x0 (proof)
Theorem b1824.. : ∀ x0 . 38635.. x0 ⟶ x0 = 39199.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 8695a.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem bcc0c.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ x4 x9 x10 = x8 x9 x10) ⟶ ∀ x9 : ι → ι . (∀ x10 . prim1 x10 x1 ⟶ x5 x10 = x9 x10) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 8695a.. (39199.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 8c11b.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 223da.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ο . ∀ x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ x4 x9 x10 = x8 x9 x10) ⟶ ∀ x9 : ι → ι . (∀ x10 . prim1 x10 x1 ⟶ x5 x10 = x9 x10) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 8c11b.. (39199.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition 1eafe.. := λ x0 . λ x1 x2 x3 : ι → ι → ι . λ x4 : ι → ι → ο . 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (eb53d.. x0 x3) (d2155.. x0 x4)))))
Theorem 223ee.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . x0 = 1eafe.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 95ea3.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . x5 x0 (f482f.. (1eafe.. x0 x1 x2 x3 x4) 4a7ef..) ⟶ x5 (f482f.. (1eafe.. x0 x1 x2 x3 x4) 4a7ef..) x0 (proof)
Theorem 9fd74.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . x0 = 1eafe.. 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 05c42.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (1eafe.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem d43b4.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . x0 = 1eafe.. 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 05f51.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (1eafe.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem f1a5f.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . x0 = 1eafe.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem db2c8.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = e3162.. (f482f.. (1eafe.. x0 x1 x2 x3 x4) (4ae4a.. (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 5aadd.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . x0 = 1eafe.. 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 35d4e.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x4 x5 x6 = 2b2e3.. (f482f.. (1eafe.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 x6 (proof)
Theorem 4a788.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 x6 x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ο . 1eafe.. x0 x2 x4 x6 x8 = 1eafe.. 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 ⟶ ∀ 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 0a9b2.. : ∀ x0 . ∀ x1 x2 x3 x4 x5 x6 : ι → ι → ι . ∀ x7 x8 : ι → ι → ο . (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x1 x9 x10 = x2 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x3 x9 x10 = x4 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x5 x9 x10 = x6 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x7 x9 x10) (x8 x9 x10)) ⟶ 1eafe.. x0 x1 x3 x5 x7 = 1eafe.. x0 x2 x4 x6 x8 (proof)
Definition 4e60e.. := 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 : ι → ι → ι . (∀ x6 . prim1 x6 x2 ⟶ ∀ x7 . prim1 x7 x2 ⟶ prim1 (x5 x6 x7) x2) ⟶ ∀ x6 : ι → ι → ο . x1 (1eafe.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 36098.. : ∀ 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 : ι → ι → ι . (∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x3 x4 x5) x0) ⟶ ∀ x4 : ι → ι → ο . 4e60e.. (1eafe.. x0 x1 x2 x3 x4) (proof)
Theorem 68c0b.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . 4e60e.. (1eafe.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 08be0.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . 4e60e.. (1eafe.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 3a31c.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . 4e60e.. (1eafe.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x3 x5 x6) x0 (proof)
Theorem 4c198.. : ∀ x0 . 4e60e.. x0 ⟶ x0 = 1eafe.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition a5367.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 2f766.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ 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) ⟶ a5367.. (1eafe.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 83aaa.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 25c57.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ 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) ⟶ 83aaa.. (1eafe.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 94613.. := λ x0 . λ x1 x2 x3 : ι → ι → ι . λ x4 : ι → ο . 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (eb53d.. x0 x3) (1216a.. x0 x4)))))
Theorem 063b4.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . x0 = 94613.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 2ab54.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . x0 = f482f.. (94613.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem f6f08.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . x0 = 94613.. 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 22e75.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (94613.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem d6c77.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . x0 = 94613.. 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 bf883.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (94613.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 5da7d.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . x0 = 94613.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem eaad1.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = e3162.. (f482f.. (94613.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem c4fb2.. : ∀ x0 x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . x0 = 94613.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 8c421.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (94613.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem 5cc8d.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 x6 x7 : ι → ι → ι . ∀ x8 x9 : ι → ο . 94613.. x0 x2 x4 x6 x8 = 94613.. 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 ⟶ ∀ 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)
Theorem 0dcb9.. : ∀ x0 . ∀ x1 x2 x3 x4 x5 x6 : ι → ι → ι . ∀ x7 x8 : ι → ο . (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x1 x9 x10 = x2 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x3 x9 x10 = x4 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x5 x9 x10 = x6 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ 94613.. x0 x1 x3 x5 x7 = 94613.. x0 x2 x4 x6 x8 (proof)
Definition 7c481.. := 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 : ι → ι → ι . (∀ x6 . prim1 x6 x2 ⟶ ∀ x7 . prim1 x7 x2 ⟶ prim1 (x5 x6 x7) x2) ⟶ ∀ x6 : ι → ο . x1 (94613.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 5c4b8.. : ∀ 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 : ι → ι → ι . (∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x3 x4 x5) x0) ⟶ ∀ x4 : ι → ο . 7c481.. (94613.. x0 x1 x2 x3 x4) (proof)
Theorem 10c49.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . 7c481.. (94613.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem fedac.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . 7c481.. (94613.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 14447.. : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . 7c481.. (94613.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x3 x5 x6) x0 (proof)
Theorem 290eb.. : ∀ x0 . 7c481.. x0 ⟶ x0 = 94613.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 9ad8d.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem ffddd.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ι . ∀ x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ 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) ⟶ 9ad8d.. (94613.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 0499f.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 61142.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ο . ∀ x1 . ∀ x2 x3 x4 : ι → ι → ι . ∀ x5 : ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ι → ι . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ 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) ⟶ 0499f.. (94613.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)