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Proofgold Signed Transaction

vin
PrJGW../01fce..
PUbX7../83d93..
vout
PrJGW../b3f54.. 1.91 bars
TMLoa../1454e.. ownership of 8aeb9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZn2../b2a25.. ownership of 2179b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFQs../65b94.. ownership of 85aab.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbkX../2ac65.. ownership of a8f87.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKAN../6347e.. ownership of 881bf.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHma../9bfa8.. ownership of 8d96d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXAt../edc0a.. ownership of 123df.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZyU../95b9a.. ownership of 0f569.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcqq../df93a.. ownership of b3a9c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZ9w../97bf0.. ownership of decfb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGSS../f78d7.. ownership of b12bd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMM8x../416a1.. ownership of 548fa.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMP8Z../0b6e0.. ownership of 06bf1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMPF../ee2f8.. ownership of 5ca5a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWj3../a04d7.. ownership of b576e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQ4E../5d38e.. ownership of 808ea.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMH1K../11ac0.. ownership of b49ff.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPYK../fade6.. ownership of 952db.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNCm../82e67.. ownership of 6df1c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYa2../41da5.. ownership of ee7ea.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdUY../fb67f.. ownership of bbde7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJh2../8c35b.. ownership of cbe34.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMX4c../bdbc8.. ownership of bbd2c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYBB../3fecb.. ownership of 2e0d7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGun../87bda.. ownership of 170ca.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGXV../8eb82.. ownership of 54368.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMEX../3be2e.. ownership of 8dad2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVTb../dcd79.. ownership of ed77c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHHD../11854.. ownership of 54d21.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZkm../f5338.. ownership of dda46.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTwS../6eb6c.. ownership of 28784.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMU7o../d0d80.. ownership of 89196.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUEM../068a6.. ownership of 747ef.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMEqC../0790d.. ownership of b7245.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKZT../3e155.. ownership of 4e086.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVKe../63917.. ownership of 85585.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJeN../f8e2b.. ownership of 5c855.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMTD../c8536.. ownership of 28b1b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUrz../45b93.. ownership of 174a4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXVF../8eaaa.. ownership of 6a233.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNy7../e8311.. ownership of 86c18.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGr8../c2561.. ownership of ba0cc.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXun../febbb.. ownership of 383cb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMmT../3864b.. ownership of 17504.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMY2Y../edd34.. ownership of 546ed.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHWZ../bc394.. ownership of 22fa5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMczH../a0977.. ownership of 68801.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWcn../d15a6.. ownership of 13a0b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMM8j../19316.. ownership of 9b563.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLZZ../418dc.. ownership of aec86.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHrS../80434.. ownership of 2a2b9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTeT../ff6f1.. ownership of e658b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLyk../0cb26.. ownership of 7f6d9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHj9../adad5.. ownership of 3bd6f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJqG../36715.. ownership of 75497.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXLV../1db17.. ownership of b8fca.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUPR../fc94a.. ownership of a70e6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVv8../a6d3a.. ownership of 18711.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGWE../147c4.. ownership of 4f5a1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLdW../f1688.. ownership of edcd7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQyz../43040.. ownership of 93dcd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMd8U../bad33.. ownership of 58966.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMair../41e22.. ownership of efe95.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGvj../93fba.. ownership of b029f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWG1../3ec54.. ownership of 895e8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMb6F../beb5b.. ownership of d9859.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNMM../45fb6.. ownership of 52ca8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKXL../79f55.. ownership of dfc2f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSQE../314fc.. ownership of 3339e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSNg../3b8a6.. ownership of 30fd3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFBR../fc73e.. ownership of 82801.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJm7../6d0eb.. ownership of fd2ef.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPb9../f5e2c.. ownership of 49df8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXK8../71b39.. ownership of fff10.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXuS../9b193.. ownership of b55f5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMToU../62d61.. ownership of 4e0a0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSQ6../8c80a.. ownership of 92cc6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMN4S../a56d6.. ownership of e76ea.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMn6../9f2d1.. ownership of 0d30e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWSG../102bf.. ownership of 9fa32.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVgM../f8b83.. ownership of 928fb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLbu../30a49.. ownership of bd647.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcap../5a476.. ownership of 117a0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJ5k../d8b64.. ownership of dc5ed.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSkX../4a275.. ownership of 6588e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMX4s../bf998.. ownership of cc1b6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWXy../4f4b4.. ownership of 567a6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbTG../4bfd2.. ownership of 3b007.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXaf../0ca56.. ownership of 7a5e3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMrK../84d6c.. ownership of de590.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLmJ../6d9e4.. ownership of 8c7f6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMY1e../0d23c.. ownership of 0f932.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMagp../83b6a.. ownership of af357.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYcS../8d01c.. ownership of 35925.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNuG../c5041.. ownership of f1c06.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbyu../878f8.. ownership of 81f50.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJur../f7c65.. ownership of aa310.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLdh../22158.. ownership of 1b187.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPUP../f463d.. ownership of 0d5f9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHsQ../466ed.. ownership of 42c25.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFwQ../7b204.. ownership of 9890e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLRc../73cc8.. ownership of 15cd9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVQa../94c1c.. ownership of b0ed2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTaR../d7941.. ownership of b07ec.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLYT../a7908.. ownership of b29ea.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZBP../11373.. ownership of 2e4ad.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXJw../caf81.. ownership of f46b1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGgg../b4285.. ownership of f31eb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKQj../2d23e.. ownership of e928d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMNg../3e42b.. ownership of bd4bd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHWR../12896.. ownership of eff65.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVCr../686c2.. ownership of e163f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWw9../ac7fd.. ownership of 3c7c5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUDV../d6198.. ownership of eff13.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPHc../79290.. ownership of bfd44.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJx2../10a0b.. ownership of 8981e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUzB../b938c.. ownership of f462c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TML8U../f4839.. ownership of 2bd07.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaBy../11c42.. ownership of d80b7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXUx../87df2.. ownership of 6b29e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRBy../281b9.. ownership of 0c169.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHAJ../a39dc.. ownership of 24266.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TML5g../f3fe2.. ownership of f3329.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTAu../953c9.. ownership of f3a12.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXAJ../82f56.. ownership of 2b252.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcVP../f6cab.. ownership of 81074.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRVb../a5038.. ownership of 3d0b4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVA4../87eec.. ownership of 94734.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMH68../48975.. ownership of 252d8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMzq../126ad.. ownership of 6a567.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRgt../9dd30.. ownership of 33e2c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaP7../99151.. ownership of b984a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQ65../ff379.. ownership of 38865.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMH2B../7f995.. ownership of 0de24.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGGy../fecf7.. ownership of 96049.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXDT../28924.. ownership of 94967.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJqa../1ae0c.. ownership of 12a13.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWFa../227dc.. ownership of abcc2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHpf../6b8f8.. ownership of 4b220.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdHW../0b9e0.. ownership of b110c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMH1k../81127.. ownership of d40c9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHre../2bf5e.. ownership of a182c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGeS../c468f.. ownership of d90ae.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNbm../acd7a.. ownership of 9d0f3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVGY../a73aa.. ownership of 22315.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGC1../4be0b.. ownership of 2f0d8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMEhX../976f3.. ownership of c2d7a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYKB../c8ecd.. ownership of ce95e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSWg../e4a53.. ownership of dcf72.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMV4V../93a49.. ownership of 59657.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKrL../6db1a.. ownership of 4f0f8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKXM../ea266.. ownership of 7f80e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMG5x../8c940.. ownership of f278f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPAP../f3477.. ownership of 946f3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYdu../7be72.. ownership of 9101a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGXc../d18ce.. ownership of 6fbca.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJaU../3959a.. ownership of a5628.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdXK../ba734.. ownership of 2150c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLHF../84151.. ownership of 27335.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdmu../49f68.. ownership of 7ba50.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMK62../246d2.. ownership of 8ccc5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaer../a5753.. ownership of 6b7bf.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXrj../b31f4.. ownership of b2295.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPuy../42e51.. ownership of e98c5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbhC../c5477.. ownership of 3c64d.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHU3../8533a.. ownership of 3e9b3.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNkd../e66a7.. ownership of adadd.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQAz../0369a.. ownership of ec7a1.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJm3../76a8b.. ownership of a3341.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbrw../91521.. ownership of 090c6.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVHB../d858e.. ownership of 5fdf5.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWhU../e4cc6.. ownership of 418e8.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWgv../e9ab0.. ownership of 86936.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWPd../edbd6.. ownership of c6a51.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZYW../304ac.. ownership of a6bc8.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVbX../289a9.. ownership of d701a.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcFa../289ef.. ownership of 42a91.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdDb../362d6.. ownership of 7ec22.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFAD../75e1d.. ownership of 96158.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNdE../fcb57.. ownership of f2f33.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMF9X../8f1bb.. ownership of dcf97.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLeM../4743f.. ownership of 350f7.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRPN../76bcd.. ownership of f4846.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSPg../36c2e.. ownership of dfba2.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHJ4../96a33.. ownership of 31bda.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMS7t../238e8.. ownership of 19c5a.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMR8i../7950f.. ownership of 33a0d.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQce../bd238.. ownership of 2861c.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFAB../68af4.. ownership of c65d4.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
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PUTJn../ee99b.. 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 b6bd3.. := λ x0 . λ x1 x2 : ι → ι → ι . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (eb53d.. x0 x2)))
Param f482f.. : ι → ι → ι
Known 52da6.. : ∀ x0 x1 x2 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 x2))) 4a7ef.. = x0
Theorem b2295.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . x0 = b6bd3.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 8ccc5.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . x0 = f482f.. (b6bd3.. x0 x1 x2) 4a7ef.. (proof)
Param e3162.. : ι → ι → ι → ι
Known c2bca.. : ∀ x0 x1 x2 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 x2))) (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 27335.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . x0 = b6bd3.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem a5628.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = e3162.. (f482f.. (b6bd3.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 x4 (proof)
Known 11d6d.. : ∀ x0 x1 x2 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) x1 x2))) (4ae4a.. (4ae4a.. 4a7ef..)) = x2
Theorem 9101a.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . x0 = b6bd3.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Theorem f278f.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x2 x3 x4 = e3162.. (f482f.. (b6bd3.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4 (proof)
Definition and := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known and3I : ∀ x0 x1 x2 : ο . x0 ⟶ x1 ⟶ x2 ⟶ and (and x0 x1) x2
Theorem 4f0f8.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι → ι . b6bd3.. x0 x2 x4 = b6bd3.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7)) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x6 x7 = x5 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 dcf72.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι → ι . (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = x2 x5 x6) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = x4 x5 x6) ⟶ b6bd3.. x0 x1 x3 = b6bd3.. x0 x2 x4 (proof)
Definition e2219.. := 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) ⟶ x1 (b6bd3.. x2 x3 x4)) ⟶ x1 x0
Theorem c2d7a.. : ∀ 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) ⟶ e2219.. (b6bd3.. x0 x1 x2) (proof)
Theorem 22315.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . e2219.. (b6bd3.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x3 x4) x0 (proof)
Theorem d90ae.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . e2219.. (b6bd3.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0 (proof)
Theorem d40c9.. : ∀ x0 . e2219.. x0 ⟶ x0 = b6bd3.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 81fc5.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 4b220.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → ι . ∀ x1 . ∀ x2 x3 : ι → ι → ι . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = x5 x6 x7) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 81fc5.. (b6bd3.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition a70ce.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 12a13.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → ο . ∀ x1 . ∀ x2 x3 : ι → ι → ι . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = x5 x6 x7) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ a70ce.. (b6bd3.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 971d3.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (0fc90.. x0 x2)))
Theorem 96049.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . x0 = 971d3.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 38865.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . x0 = f482f.. (971d3.. x0 x1 x2) 4a7ef.. (proof)
Theorem 33e2c.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . x0 = 971d3.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem 252d8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = e3162.. (f482f.. (971d3.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 x4 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 3d0b4.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . x0 = 971d3.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ x3 x4 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 2b252.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 . prim1 x3 x0 ⟶ x2 x3 = f482f.. (f482f.. (971d3.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 (proof)
Theorem f3329.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι . 971d3.. x0 x2 x4 = 971d3.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7)) (∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6) (proof)
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Theorem 0c169.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι . (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = x2 x5 x6) ⟶ (∀ x5 . prim1 x5 x0 ⟶ x3 x5 = x4 x5) ⟶ 971d3.. x0 x1 x3 = 971d3.. x0 x2 x4 (proof)
Definition a5e4b.. := 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) ⟶ x1 (971d3.. x2 x3 x4)) ⟶ x1 x0
Theorem d80b7.. : ∀ 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) ⟶ a5e4b.. (971d3.. x0 x1 x2) (proof)
Theorem f462c.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . a5e4b.. (971d3.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x3 x4) x0 (proof)
Theorem bfd44.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . a5e4b.. (971d3.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0 (proof)
Theorem 3c7c5.. : ∀ x0 . a5e4b.. x0 ⟶ x0 = 971d3.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition ccf31.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem eff65.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ ccf31.. (971d3.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition f4433.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem e928d.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ f4433.. (971d3.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition b5cc3.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (d2155.. x0 x2)))
Theorem f46b1.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . x0 = b5cc3.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem b29ea.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 x3 : ι → ι → ο . x3 x0 (f482f.. (b5cc3.. x0 x1 x2) 4a7ef..) ⟶ x3 (f482f.. (b5cc3.. x0 x1 x2) 4a7ef..) x0 (proof)
Theorem b0ed2.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . x0 = b5cc3.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem 9890e.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = e3162.. (f482f.. (b5cc3.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 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 0d5f9.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . x0 = b5cc3.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x4 x5 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Theorem aa310.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x2 x3 x4 = 2b2e3.. (f482f.. (b5cc3.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4 (proof)
Theorem f1c06.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . b5cc3.. x0 x2 x4 = b5cc3.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7)) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x4 x6 x7 = x5 x6 x7) (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
Theorem af357.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = x2 x5 x6) ⟶ (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ iff (x3 x5 x6) (x4 x5 x6)) ⟶ b5cc3.. x0 x1 x3 = b5cc3.. x0 x2 x4 (proof)
Definition ec962.. := 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 . x1 (b5cc3.. x2 x3 x4)) ⟶ x1 x0
Theorem 8c7f6.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ο . ec962.. (b5cc3.. x0 x1 x2) (proof)
Theorem 7a5e3.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ec962.. (b5cc3.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x3 x4) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 567a6.. : ∀ x0 . ec962.. x0 ⟶ x0 = b5cc3.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 68fde.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 6588e.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x3 x6 x7) (x5 x6 x7)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 68fde.. (b5cc3.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition c65d4.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 117a0.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x3 x6 x7) (x5 x6 x7)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ c65d4.. (b5cc3.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Param 1216a.. : ι → (ι → ο) → ι
Definition 33a0d.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) (1216a.. x0 x2)))
Theorem 928fb.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . x0 = 33a0d.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 0d30e.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . x0 = f482f.. (33a0d.. x0 x1 x2) 4a7ef.. (proof)
Theorem 92cc6.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . x0 = 33a0d.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem b55f5.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = e3162.. (f482f.. (33a0d.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 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 49df8.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . x0 = 33a0d.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ x3 x4 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 82801.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 . prim1 x3 x0 ⟶ x2 x3 = decode_p (f482f.. (33a0d.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 (proof)
Theorem 3339e.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . 33a0d.. x0 x2 x4 = 33a0d.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7)) (∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6) (proof)
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Theorem 52ca8.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . (∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = x2 x5 x6) ⟶ (∀ x5 . prim1 x5 x0 ⟶ iff (x3 x5) (x4 x5)) ⟶ 33a0d.. x0 x1 x3 = 33a0d.. x0 x2 x4 (proof)
Definition 31bda.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ο . x1 (33a0d.. x2 x3 x4)) ⟶ x1 x0
Theorem 895e8.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ο . 31bda.. (33a0d.. x0 x1 x2) (proof)
Theorem efe95.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . 31bda.. (33a0d.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x3 x4) x0 (proof)
Theorem 93dcd.. : ∀ x0 . 31bda.. x0 ⟶ x0 = 33a0d.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition f4846.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 4f5a1.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ f4846.. (33a0d.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition dcf97.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem a70e6.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ dcf97.. (33a0d.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 96158.. := λ x0 . λ x1 : ι → ι → ι . λ x2 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (eb53d.. x0 x1) x2))
Theorem 75497.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 . x0 = 96158.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 7f6d9.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . x0 = f482f.. (96158.. x0 x1 x2) 4a7ef.. (proof)
Theorem 2a2b9.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 . x0 = 96158.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x4 x5 (proof)
Theorem 9b563.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = e3162.. (f482f.. (96158.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 x4 (proof)
Theorem 68801.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 . x0 = 96158.. x1 x2 x3 ⟶ x3 = f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)) (proof)
Theorem 546ed.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . x2 = f482f.. (96158.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..)) (proof)
Theorem 383cb.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . 96158.. x0 x2 x4 = 96158.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x2 x6 x7 = x3 x6 x7)) (x4 = x5) (proof)
Theorem 86c18.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 . (∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = x2 x4 x5) ⟶ 96158.. x0 x1 x3 = 96158.. x0 x2 x3 (proof)
Definition 42a91.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 . prim1 x4 x2 ⟶ x1 (96158.. x2 x3 x4)) ⟶ x1 x0
Theorem 174a4.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 . prim1 x2 x0 ⟶ 42a91.. (96158.. x0 x1 x2) (proof)
Theorem 5c855.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . 42a91.. (96158.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x3 x4) x0 (proof)
Theorem 4e086.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . 42a91.. (96158.. x0 x1 x2) ⟶ prim1 x2 x0 (proof)
Theorem 747ef.. : ∀ x0 . 42a91.. x0 ⟶ x0 = 96158.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Definition a6bc8.. := λ x0 . λ x1 : ι → (ι → ι → ι) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))
Theorem 28784.. : ∀ x0 : ι → (ι → ι → ι) → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3) ⟶ a6bc8.. (96158.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 86936.. := λ x0 . λ x1 : ι → (ι → ι → ι) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))
Theorem 54d21.. : ∀ x0 : ι → (ι → ι → ι) → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 . (∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = x4 x5 x6) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3) ⟶ 86936.. (96158.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 5fdf5.. := λ x0 . λ x1 x2 : ι → ι . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (λ x3 . If_i (x3 = 4a7ef..) x0 (If_i (x3 = 4ae4a.. 4a7ef..) (0fc90.. x0 x1) (0fc90.. x0 x2)))
Theorem 8dad2.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . x0 = 5fdf5.. x1 x2 x3 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 170ca.. : ∀ x0 . ∀ x1 x2 : ι → ι . x0 = f482f.. (5fdf5.. x0 x1 x2) 4a7ef.. (proof)
Theorem bbd2c.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . x0 = 5fdf5.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ x2 x4 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x4 (proof)
Theorem bbde7.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . prim1 x3 x0 ⟶ x1 x3 = f482f.. (f482f.. (5fdf5.. x0 x1 x2) (4ae4a.. 4a7ef..)) x3 (proof)
Theorem 6df1c.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . x0 = 5fdf5.. x1 x2 x3 ⟶ ∀ x4 . prim1 x4 x1 ⟶ x3 x4 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem b49ff.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . prim1 x3 x0 ⟶ x2 x3 = f482f.. (f482f.. (5fdf5.. x0 x1 x2) (4ae4a.. (4ae4a.. 4a7ef..))) x3 (proof)
Theorem b576e.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . 5fdf5.. x0 x2 x4 = 5fdf5.. x1 x3 x5 ⟶ and (and (x0 = x1) (∀ x6 . prim1 x6 x0 ⟶ x2 x6 = x3 x6)) (∀ x6 . prim1 x6 x0 ⟶ x4 x6 = x5 x6) (proof)
Theorem 06bf1.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . (∀ x5 . prim1 x5 x0 ⟶ x1 x5 = x2 x5) ⟶ (∀ x5 . prim1 x5 x0 ⟶ x3 x5 = x4 x5) ⟶ 5fdf5.. x0 x1 x3 = 5fdf5.. x0 x2 x4 (proof)
Definition a3341.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ x1 (5fdf5.. x2 x3 x4)) ⟶ x1 x0
Theorem b12bd.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ a3341.. (5fdf5.. x0 x1 x2) (proof)
Theorem b3a9c.. : ∀ x0 . ∀ x1 x2 : ι → ι . a3341.. (5fdf5.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x3) x0 (proof)
Theorem 123df.. : ∀ x0 . ∀ x1 x2 : ι → ι . a3341.. (5fdf5.. x0 x1 x2) ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0 (proof)
Theorem 881bf.. : ∀ x0 . a3341.. x0 ⟶ x0 = 5fdf5.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition adadd.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 85aab.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → ι . ∀ x1 . ∀ x2 x3 : ι → ι . (∀ x4 : ι → ι . (∀ x5 . prim1 x5 x1 ⟶ x2 x5 = x4 x5) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ adadd.. (5fdf5.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)
Definition 3c64d.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 8aeb9.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → ο . ∀ x1 . ∀ x2 x3 : ι → ι . (∀ x4 : ι → ι . (∀ x5 . prim1 x5 x1 ⟶ x2 x5 = x4 x5) ⟶ ∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x3 x6 = x5 x6) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3) ⟶ 3c64d.. (5fdf5.. x1 x2 x3) x0 = x0 x1 x2 x3 (proof)