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Proofgold Signed Transaction

vin
PrQe3../e1748..
PUfAD../c4863..
vout
PrQe3../11ee0.. 24.99 bars
TMFTB../e4972.. ownership of 36c69.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPp8../2d625.. ownership of 0994b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPLV../f0c4a.. ownership of 74618.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMmG../31b4b.. ownership of 615fb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYTe../64e93.. ownership of fb3e6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMR3A../fd3b7.. ownership of e8caf.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYZH../1cb4f.. ownership of 4e03a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQaV../67498.. ownership of e29f5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRtF../7d82a.. ownership of d9111.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNnK../630ed.. ownership of 5743d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWos../d7be5.. ownership of 38e53.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZDZ../7d773.. ownership of c5708.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGbd../ba678.. ownership of 6f842.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVuR../dcc5c.. ownership of 916ea.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdWb../dfb94.. ownership of 87289.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWdv../e0304.. ownership of 8b89c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcLx../7fc16.. ownership of 6f78f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMStL../a5724.. ownership of 87dbd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXb8../de847.. ownership of b9d33.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPJz../5affe.. ownership of 40771.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNoX../4fcd3.. ownership of b9667.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQW2../79855.. ownership of 982af.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbom../b1b0f.. ownership of e662d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYj7../3288d.. ownership of 82f0f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMY7t../230f8.. ownership of ffb92.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaLz../09132.. ownership of ac822.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQuR../ee3df.. ownership of 5254a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKs7../fac99.. ownership of 28402.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMX4b../0e3d4.. ownership of 00164.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRdK../87fa6.. ownership of 1c09d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTe9../6ea2b.. ownership of f7a25.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMW7M../90036.. ownership of 49336.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMK3A../1320d.. ownership of 590ce.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMb4T../10939.. ownership of 860ef.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQoK../0136a.. ownership of 114cc.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPyC../49c0c.. ownership of 25e22.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMc3d../8ebb3.. ownership of 83897.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRuH../d2a28.. ownership of d71f4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMV81../8722a.. ownership of 78290.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMN7j../7813b.. ownership of ae7b4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFs4../5a328.. ownership of 630ad.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUyE../9addb.. ownership of e24dc.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaPL../8e1ab.. ownership of 9b099.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbFF../9c8a1.. ownership of 7d695.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTqt../941a5.. ownership of 5c0c3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYBu../032fb.. ownership of ca700.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNdP../57359.. ownership of 986ac.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWm6../5d2cd.. ownership of 64c63.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFMu../48ea4.. ownership of bb207.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSFc../726c9.. ownership of 840c7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZgG../03be1.. ownership of f0b6a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaE9../1b801.. ownership of 2ff6f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdNM../cad4e.. ownership of 1a4cb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcej../789e9.. ownership of 90f58.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMV8i../f1a2e.. ownership of 6c23d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQKC../b0a1c.. ownership of 74e84.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSwt../9ff8b.. ownership of 6425a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVib../5b4dd.. ownership of dd186.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMExd../8731b.. ownership of 6f593.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMDV../0a5c5.. ownership of 872a5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVU3../d38d0.. ownership of 92643.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNyh../73742.. ownership of 4998f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZMS../42a72.. ownership of dfafe.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLSU../588da.. ownership of de92d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTn8../82413.. ownership of 8f50d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUwg../671bb.. ownership of f27d5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKSn../46a91.. ownership of 2fd40.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMF7U../59111.. ownership of f62a2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMU3g../6faf4.. ownership of 637a6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVQw../507c5.. ownership of 939e0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXmc../478de.. ownership of a43d0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUtx../f2d40.. ownership of 0ca63.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRVE../9a7fd.. ownership of 4957e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQ8d../c77aa.. ownership of 951ba.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUqa../a3436.. ownership of 4abe4.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLx7../2f20e.. ownership of 54a2e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMKQ../7ac8b.. ownership of d6b4d.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbGS../2bfcc.. ownership of 8594f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWBe../09095.. ownership of 83984.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMW7w../9b02e.. ownership of 3ad06.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMbfV../a5832.. ownership of a0ae9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaoW../884f6.. ownership of 1fb88.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPAG../42ef7.. ownership of ffd34.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGCh../35904.. ownership of 55e99.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMuz../bfda6.. ownership of 428c8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMNs../ada26.. ownership of 3ff32.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMW6u../03849.. ownership of c00a9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMT4m../cbcd0.. ownership of 707e1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMF2p../abdae.. ownership of 0f3fa.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNN1../7b663.. ownership of 8a974.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRJN../a0dcc.. ownership of e5917.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWGS../3e391.. ownership of c2318.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJkc../5af94.. ownership of 85096.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPDC../5a011.. ownership of 11341.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdDU../0b3be.. ownership of d3666.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMqi../87abf.. ownership of d0c66.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZoj../27048.. ownership of 23bd6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMF1g../ff55d.. ownership of 8f17a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRpv../a8bee.. ownership of 9d5e6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMR9a../02cc8.. ownership of 525d1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLzn../f1276.. ownership of fe575.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdxh../95f52.. ownership of 406dd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGCU../f4514.. ownership of cc1ac.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSrz../b4a96.. ownership of 4ef99.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMS3y../f2c04.. ownership of b32dd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGmp../35327.. ownership of f9785.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMK68../1729d.. ownership of 5928f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTAb../a4789.. ownership of a28c9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKon../612c8.. ownership of 06a3b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMckJ../75c1b.. ownership of c80bd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHCb../86388.. ownership of 14318.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMV6m../afc50.. ownership of 2a58f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVH6../4cddf.. ownership of ccbda.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMV9E../f9059.. ownership of ac19c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQ2E../cfe30.. ownership of 3dd89.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHtp../4a89c.. ownership of cdda7.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSZ8../1b2ba.. ownership of 1e34f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHwc../77ef7.. ownership of 95249.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMR3Y../7ac7c.. ownership of 6382b.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZJ6../7fe9f.. ownership of 92ebd.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TML2j../5e59e.. ownership of 208da.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMY5U../89ec4.. ownership of 3ae86.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWma../0c601.. ownership of ee439.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMK2w../82a6d.. ownership of 83df2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFDS../881a0.. ownership of 68ea5.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTbC../ae16b.. ownership of bea58.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTGr../ce853.. ownership of 1d6f8.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaAW../37560.. ownership of 848a1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXem../2faa4.. ownership of adcff.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWic../a4c46.. ownership of d8e00.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcCS../dbe89.. ownership of acc69.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYKA../4e730.. ownership of 379bb.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcSE../f9be1.. ownership of 5de34.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMb7N../b77ac.. ownership of 687a2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMYbu../479f7.. ownership of 0dd31.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWuW../6ad0d.. ownership of 73d1f.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUFP../79950.. ownership of b2090.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMXDD../5388d.. ownership of 9221a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTkA../5796f.. ownership of 90ad0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMKnY../f5020.. ownership of 97af6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNni../e47db.. ownership of 91375.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMP97../e61da.. ownership of 4cee2.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMTAs../eb87a.. ownership of 7e5c6.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLoS../4bc59.. ownership of 31346.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMP97../6b26c.. ownership of 7d9db.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMWKt../63e67.. ownership of 042a1.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVnS../161af.. ownership of da287.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMLf../071ee.. ownership of c215c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaze../6ca33.. ownership of 06e3e.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdZz../d8f3a.. ownership of f5e8a.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGQg../620ea.. ownership of 9bf50.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMD6../cb40d.. ownership of e5733.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVTT../d4d2c.. ownership of 0ad7c.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFQY../abf33.. ownership of 74cfa.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMUS2../27549.. ownership of 1a809.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGRQ../3f531.. ownership of f06b0.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMc8v../56f10.. ownership of 58d81.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVQK../c95f8.. ownership of 9f8e9.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TML3u../df4ab.. ownership of ca5f3.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJCM../c72f7.. ownership of 42a09.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMS1Y../0ee3a.. ownership of 55222.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRqS../1ce68.. ownership of 7ce35.. as prop with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSPt../22ca3.. ownership of 98b20.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMQ1V../7bee4.. ownership of e7259.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGoZ../eb7e2.. ownership of 7c58a.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMaVK../93ebb.. ownership of 291df.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGyb../59b29.. ownership of 883b9.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVgu../cb625.. ownership of 0bccc.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMPiw../77eaa.. ownership of 5f184.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMdH5../1e51c.. ownership of 9e274.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMW6a../baa9d.. ownership of b41b9.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMVpm../a5d63.. ownership of b3d95.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRBT../69574.. ownership of 84815.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMMKG../d9a1f.. ownership of bbe68.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMcwz../6c98b.. ownership of bfe00.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMZzF../01f5e.. ownership of 16a11.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMHFr../4ab76.. ownership of 7ba51.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMGvn../54b91.. ownership of baa23.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJTb../2658f.. ownership of 8f2fa.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMc1U../13aef.. ownership of f7be1.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMK79../b8f11.. ownership of 5ad38.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMLW8../5dc62.. ownership of 53f81.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMNPS../a0b27.. ownership of 24591.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSEB../3966c.. ownership of 45888.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMb8J../dd6d0.. ownership of 942b6.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMJry../587b5.. ownership of 4c338.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMRbv../05203.. ownership of dd052.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMSdW../494e2.. ownership of 4ea86.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
TMFiJ../b1081.. ownership of 6f238.. as obj with payaddr PrGxv.. rightscost 0.00 controlledby PrGxv.. upto 0
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PUYZk../7e764.. doc published by PrGxv..
Param 0fc90.. : ι → (ι → ι) → ι
Param 4ae4a.. : ι → ι
Param 4a7ef.. : ι
Param If_i : ο → ι → ι → ι
Param eb53d.. : ι → CT2 ι
Param d2155.. : ι → (ι → ι → ο) → ι
Definition 4d5a4.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι → ο . 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..)) (d2155.. 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 55222.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = 4d5a4.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem ca5f3.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 . x0 = f482f.. (4d5a4.. 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 58d81.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = 4d5a4.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 1a809.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (4d5a4.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (proof)
Param 2b2e3.. : ι → ι → ι → ο
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
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 0ad7c.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = 4d5a4.. 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 9bf50.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = 2b2e3.. (f482f.. (4d5a4.. 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 06e3e.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = 4d5a4.. x1 x2 x3 x4 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem da287.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 . x3 = f482f.. (4d5a4.. 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 7d9db.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 . 4d5a4.. x0 x2 x4 x6 = 4d5a4.. 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)
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 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 7e5c6.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x1 x6 x7 = x2 x6 x7) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ iff (x3 x6 x7) (x4 x6 x7)) ⟶ 4d5a4.. x0 x1 x3 x5 = 4d5a4.. x0 x2 x4 x5 (proof)
Definition 95b66.. := 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 . prim1 x5 x2 ⟶ x1 (4d5a4.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 91375.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ο . ∀ x3 . prim1 x3 x0 ⟶ 95b66.. (4d5a4.. x0 x1 x2 x3) (proof)
Theorem 90ad0.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 . 95b66.. (4d5a4.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem b2090.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 . 95b66.. (4d5a4.. x0 x1 x2 x3) ⟶ prim1 x3 x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 0dd31.. : ∀ x0 . 95b66.. x0 ⟶ x0 = 4d5a4.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition b1285.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 5de34.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . (∀ 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)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ b1285.. (4d5a4.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 83f8d.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem acc69.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . (∀ 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)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 83f8d.. (4d5a4.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Param 1216a.. : ι → (ι → ο) → ι
Definition 60b2c.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ο . 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..)) (1216a.. x0 x2) x3)))
Theorem adcff.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = 60b2c.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 1d6f8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 . x0 = f482f.. (60b2c.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem 68ea5.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = 60b2c.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x2 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem ee439.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x1 x4 x5 = e3162.. (f482f.. (60b2c.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 x5 (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 208da.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = 60b2c.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 6382b.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 x4 . prim1 x4 x0 ⟶ x2 x4 = decode_p (f482f.. (60b2c.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 1e34f.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = 60b2c.. x1 x2 x3 x4 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 3dd89.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 . x3 = f482f.. (60b2c.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem ccbda.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . ∀ x6 x7 . 60b2c.. x0 x2 x4 x6 = 60b2c.. 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)
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Theorem 14318.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x1 x6 x7 = x2 x6 x7) ⟶ (∀ x6 . prim1 x6 x0 ⟶ iff (x3 x6) (x4 x6)) ⟶ 60b2c.. x0 x1 x3 x5 = 60b2c.. x0 x2 x4 x5 (proof)
Definition 1c3d6.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x2 ⟶ x1 (60b2c.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 06a3b.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ο . ∀ x3 . prim1 x3 x0 ⟶ 1c3d6.. (60b2c.. x0 x1 x2 x3) (proof)
Theorem 5928f.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 . 1c3d6.. (60b2c.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x1 x4 x5) x0 (proof)
Theorem b32dd.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ο . ∀ x3 . 1c3d6.. (60b2c.. x0 x1 x2 x3) ⟶ prim1 x3 x0 (proof)
Theorem cc1ac.. : ∀ x0 . 1c3d6.. x0 ⟶ x0 = 60b2c.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 6f238.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem fe575.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ο) → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ο . (∀ x7 . prim1 x7 x1 ⟶ iff (x3 x7) (x6 x7)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 6f238.. (60b2c.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition dd052.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 9d5e6.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ο) → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . (∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = x5 x6 x7) ⟶ ∀ x6 : ι → ο . (∀ x7 . prim1 x7 x1 ⟶ iff (x3 x7) (x6 x7)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ dd052.. (60b2c.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 942b6.. := λ x0 . λ x1 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..) (0fc90.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (d2155.. x0 x3))))
Theorem 23bd6.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = 942b6.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem d3666.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . x4 x0 (f482f.. (942b6.. x0 x1 x2 x3) 4a7ef..) ⟶ x4 (f482f.. (942b6.. x0 x1 x2 x3) 4a7ef..) x0 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 85096.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = 942b6.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x5 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem e5917.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x1 x4 = f482f.. (f482f.. (942b6.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 0f3fa.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = 942b6.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem c00a9.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x2 x4 = f482f.. (f482f.. (942b6.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 428c8.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . x0 = 942b6.. 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 ffd34.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x3 x4 x5 = 2b2e3.. (f482f.. (942b6.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 x5 (proof)
Theorem a0ae9.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . 942b6.. x0 x2 x4 x6 = 942b6.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x6 x8 x9 = x7 x8 x9) (proof)
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Theorem 83984.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . ∀ x5 x6 : ι → ι → ο . (∀ x7 . prim1 x7 x0 ⟶ x1 x7 = x2 x7) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x3 x7 = x4 x7) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (x5 x7 x8) (x6 x7 x8)) ⟶ 942b6.. x0 x1 x3 x5 = 942b6.. x0 x2 x4 x6 (proof)
Definition 24591.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ι → ο . x1 (942b6.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem d6b4d.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ι → ο . 24591.. (942b6.. x0 x1 x2 x3) (proof)
Theorem 4abe4.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . 24591.. (942b6.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x4) x0 (proof)
Theorem 4957e.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ι → ο . 24591.. (942b6.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 (proof)
Theorem a43d0.. : ∀ x0 . 24591.. x0 ⟶ x0 = 942b6.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 5ad38.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 637a6.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . (∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x2 x6 = x5 x6) ⟶ ∀ 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) ⟶ 5ad38.. (942b6.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 8f2fa.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 2fd40.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ι → ο . (∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x2 x6 = x5 x6) ⟶ ∀ 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) ⟶ 8f2fa.. (942b6.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 7ba51.. := λ x0 . λ x1 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..) (0fc90.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (1216a.. x0 x3))))
Theorem 8f50d.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ο . x0 = 7ba51.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem dfafe.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ο . x0 = f482f.. (7ba51.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem 92643.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ο . x0 = 7ba51.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x5 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 6f593.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x1 x4 = f482f.. (f482f.. (7ba51.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 6425a.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ο . x0 = 7ba51.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 6c23d.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x2 x4 = f482f.. (f482f.. (7ba51.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem 1a4cb.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ο . x0 = 7ba51.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x4 x5 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem f0b6a.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x3 x4 = decode_p (f482f.. (7ba51.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (proof)
Theorem bb207.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . ∀ x6 x7 : ι → ο . 7ba51.. x0 x2 x4 x6 = 7ba51.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8)) (∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8) (proof)
Theorem 986ac.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . ∀ x5 x6 : ι → ο . (∀ x7 . prim1 x7 x0 ⟶ x1 x7 = x2 x7) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x3 x7 = x4 x7) ⟶ (∀ x7 . prim1 x7 x0 ⟶ iff (x5 x7) (x6 x7)) ⟶ 7ba51.. x0 x1 x3 x5 = 7ba51.. x0 x2 x4 x6 (proof)
Definition bfe00.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ο . x1 (7ba51.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 5c0c3.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ο . bfe00.. (7ba51.. x0 x1 x2 x3) (proof)
Theorem 9b099.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ο . bfe00.. (7ba51.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x4) x0 (proof)
Theorem 630ad.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 : ι → ο . bfe00.. (7ba51.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 (proof)
Theorem 78290.. : ∀ x0 . bfe00.. x0 ⟶ x0 = 7ba51.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 84815.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 83897.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ο) → ι . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ο . (∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x2 x6 = x5 x6) ⟶ ∀ 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) ⟶ 84815.. (7ba51.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition b41b9.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 114cc.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → (ι → ο) → ο . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 : ι → ο . (∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x2 x6 = x5 x6) ⟶ ∀ 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) ⟶ b41b9.. (7ba51.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 5f184.. := λ x0 . λ x1 x2 : ι → ι . λ x3 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (0fc90.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) x3)))
Theorem 590ce.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 . x0 = 5f184.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem f7a25.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . x0 = f482f.. (5f184.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem 00164.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 . x0 = 5f184.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x5 = f482f.. (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 5254a.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ x1 x4 = f482f.. (f482f.. (5f184.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Theorem ffb92.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 . x0 = 5f184.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x3 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem e662d.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ x2 x4 = f482f.. (f482f.. (5f184.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 (proof)
Theorem b9667.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι . ∀ x4 . x0 = 5f184.. x1 x2 x3 x4 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem b9d33.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . x3 = f482f.. (5f184.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 6f78f.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι . ∀ x6 x7 . 5f184.. x0 x2 x4 x6 = 5f184.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 . prim1 x8 x0 ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ x4 x8 = x5 x8)) (x6 = x7) (proof)
Theorem 87289.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι . ∀ x5 . (∀ x6 . prim1 x6 x0 ⟶ x1 x6 = x2 x6) ⟶ (∀ x6 . prim1 x6 x0 ⟶ x3 x6 = x4 x6) ⟶ 5f184.. x0 x1 x3 x5 = 5f184.. x0 x2 x4 x5 (proof)
Definition 883b9.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x2 ⟶ prim1 (x3 x4) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 . prim1 x5 x2 ⟶ x1 (5f184.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 6f842.. : ∀ x0 . ∀ x1 : ι → ι . (∀ x2 . prim1 x2 x0 ⟶ prim1 (x1 x2) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 . prim1 x3 x0 ⟶ 883b9.. (5f184.. x0 x1 x2 x3) (proof)
Theorem 38e53.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . 883b9.. (5f184.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x1 x4) x0 (proof)
Theorem d9111.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . 883b9.. (5f184.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x4) x0 (proof)
Theorem 4e03a.. : ∀ x0 . ∀ x1 x2 : ι → ι . ∀ x3 . 883b9.. (5f184.. x0 x1 x2 x3) ⟶ prim1 x3 x0 (proof)
Theorem fb3e6.. : ∀ x0 . 883b9.. x0 ⟶ x0 = 5f184.. (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition 7c58a.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → ι → ι . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 74618.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 . (∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x2 x6 = x5 x6) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 7c58a.. (5f184.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 98b20.. := λ x0 . λ x1 : ι → (ι → ι) → (ι → ι) → ι → ο . x1 (f482f.. x0 4a7ef..) (f482f.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))
Theorem 36c69.. : ∀ x0 : ι → (ι → ι) → (ι → ι) → ι → ο . ∀ x1 . ∀ x2 x3 : ι → ι . ∀ x4 . (∀ x5 : ι → ι . (∀ x6 . prim1 x6 x1 ⟶ x2 x6 = x5 x6) ⟶ ∀ x6 : ι → ι . (∀ x7 . prim1 x7 x1 ⟶ x3 x7 = x6 x7) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 98b20.. (5f184.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)