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Proofgold Signed Transaction

vin
PrQZh../119f3..
PUWXe../a0b0f..
vout
PrQZh../bdd48.. 24.98 bars
TMcTB../e4986.. ownership of caeb2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG9K../a15d6.. ownership of ab5e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZf9../f9500.. ownership of 9e0ff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdJe../8f4fe.. ownership of 59b6b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdef../72696.. ownership of 3f026.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW4k../1c71c.. ownership of eaff8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPfG../1833a.. ownership of 58b23.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSAW../92c7d.. ownership of b5f54.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHEr../9ea43.. ownership of 30c66.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHaH../648eb.. ownership of c2445.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXPZ../0eab1.. ownership of 2f911.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaMX../36c48.. ownership of 6b137.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF2s../5d3f9.. ownership of c0c2b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX6G../ad766.. ownership of 2def7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJxD../de91c.. ownership of c22ae.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLGc../ae640.. ownership of 7c9c9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZYa../92171.. ownership of bcf71.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEyu../06d24.. ownership of 0399c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY92../bbcc0.. ownership of fa07e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcFc../aceb7.. ownership of ec3a8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGE6../d8de6.. ownership of 7173f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTUq../19267.. ownership of e8a63.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZqH../75b6b.. ownership of 0f0c4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFuZ../2e56c.. ownership of 96b84.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY7F../6ae4d.. ownership of 6d328.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMckR../aedac.. ownership of a57fb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWS9../24033.. ownership of 0a284.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNfZ../4e914.. ownership of defbe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd2T../d769f.. ownership of 9c9ff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFAx../f464e.. ownership of 52d1e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUnb../a916f.. ownership of af941.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFH7../93dbc.. ownership of a6d08.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMS3Q../b6a0f.. ownership of 6998e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRHB../44f4f.. ownership of 6b51c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUSL../4101b.. ownership of 1eb75.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVkn../5644b.. ownership of eb65d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcWv../e8bf2.. ownership of 5ba00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVoG../838ee.. ownership of 2c522.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPNc../044ec.. ownership of ae43e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTB8../0b0fe.. ownership of 6f101.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNA7../d0620.. ownership of 6c39d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcxJ../ec424.. ownership of effb5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUqL../ca0a9.. ownership of 402fa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZdZ../e0cfe.. ownership of 8ca38.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNVT../08c37.. ownership of da0e2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLad../3a19c.. ownership of 19661.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX6s../d234d.. ownership of 08cf8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKGp../6288d.. ownership of a6fb7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU8k../4cb69.. ownership of a72a6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYD2../aa9c8.. ownership of e6177.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFky../26c6f.. ownership of 24d22.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZZ5../d33b8.. ownership of 226a6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUCP../f1198.. ownership of 5753b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTXz../c9822.. ownership of 53e6d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLRx../fe07d.. ownership of 56b62.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJGJ../929c3.. ownership of bcf04.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ1o../89633.. ownership of c7eb2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaQb../262d0.. ownership of 38922.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEvf../a3ed6.. ownership of 8d5fd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdVT../a64cf.. ownership of 80400.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWth../9a6be.. ownership of 1c594.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTcm../38849.. ownership of c6695.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPyU../ebfb2.. ownership of b21e7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUxq../130d8.. ownership of 66066.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMcS../c52ca.. ownership of cd382.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHVH../cff44.. ownership of 08bd9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcK8../a5608.. ownership of 96968.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbkj../035ee.. ownership of 56062.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNFZ../646c9.. ownership of 4bb01.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMhu../f7a3e.. ownership of 60e12.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdED../7705b.. ownership of 3c3d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGQf../3d71d.. ownership of 31b72.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGuL../aa999.. ownership of 13766.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJDo../c7be1.. ownership of 35148.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEmk../349c7.. ownership of d409f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF99../e46be.. ownership of e997a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJWt../8d3b6.. ownership of 5da3a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRcG../c4f4e.. ownership of c49d7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLrh../cf476.. ownership of a85d0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTD6../073cc.. ownership of f914d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFMW../34268.. ownership of 04af0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbY8../48135.. ownership of 54c5f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZC3../53297.. ownership of 18431.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXrm../acf9e.. ownership of 8cd9f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGDs../3c01f.. ownership of d3e57.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGqy../52e26.. ownership of 651be.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXsd../acb72.. ownership of 4f115.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLJF../d09fa.. ownership of 1c9af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKRQ../8cef6.. ownership of 7bb35.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLuK../831ba.. ownership of d5418.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd5m../dd6d6.. ownership of afc32.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV7d../45192.. ownership of 1c3bf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUFd../50349.. ownership of bedba.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFZf../5dd38.. ownership of 84726.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQHm../f11de.. ownership of c5e5b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU9W../f2d42.. ownership of c495c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVn6../ecd50.. ownership of 546c0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbm3../1388e.. ownership of d0027.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN52../2d8dc.. ownership of 8d565.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLAE../54a56.. ownership of fa49a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaX6../4aee4.. ownership of 2f459.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHad../2043c.. ownership of 89352.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSAH../e77af.. ownership of 6bf38.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKD7../d10c3.. ownership of e92e7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN8S../0957a.. ownership of 4d890.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaU2../36c63.. ownership of 65cce.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQu3../9ea5e.. ownership of e31dc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNFs../402fd.. ownership of 757d9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZpe../f8a71.. ownership of 3a7bb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWKa../b5775.. ownership of b55b7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdHt../c8bab.. ownership of 7046d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRUE../ab366.. ownership of a4f71.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGgk../4f703.. ownership of 75cc6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNhH../98d83.. ownership of 77dc4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXvk../33a6d.. ownership of 0d70c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHsL../2bb81.. ownership of 44535.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbJW../ac984.. ownership of 4344e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGEJ../be31a.. ownership of 1a15d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZXw../ec8c7.. ownership of a7310.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUT5../8da02.. ownership of 82530.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdGj../5fa3e.. ownership of b1e5b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN1v../eea4b.. ownership of 65aa0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbNv../98aab.. ownership of 6944d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcsU../1540a.. ownership of c34a2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTKp../a91ae.. ownership of 77353.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLnQ../f09bd.. ownership of b64db.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbqB../ec47d.. ownership of 46d59.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRDa../ae033.. ownership of ed9d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZgR../d01a0.. ownership of e347f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXAj../79cc3.. ownership of 95a0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXa6../2eafd.. ownership of 8844f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb9R../1cd83.. ownership of 361f5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd1L../8327d.. ownership of 1d7a9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGYE../7692a.. ownership of f2aa8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXAG../5166d.. ownership of 6ffdb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHfW../48e24.. ownership of b8b08.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYHY../9a216.. ownership of ec944.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR26../b5a27.. ownership of 13cdc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQAY../eb7b0.. ownership of e1561.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMauf../b5726.. ownership of 17bfe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKot../d53fd.. ownership of 0edec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSsz../24362.. ownership of abc6a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFHL../72c0c.. ownership of 0d56c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT57../977d5.. ownership of 39286.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRyf../ff5e2.. ownership of cd973.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJPQ../2ec7c.. ownership of c8f16.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXfU../ac754.. ownership of 49161.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcUR../1ec9f.. ownership of 53d29.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRDQ../8bc4d.. ownership of 34992.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT3o../4dd94.. ownership of 7f2dd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXkU../69913.. ownership of 3b3d8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ3T../e5ec4.. ownership of 9d561.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHMo../2a761.. ownership of d0646.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHp1../8d17d.. ownership of a6a5b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKEq../9d72a.. ownership of 8b540.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLe1../74a4d.. ownership of 2bf57.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbp1../72f98.. ownership of 6b0a5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ3o../6902c.. ownership of 570a1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQT9../a4e33.. ownership of 971dc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ8V../fd58f.. ownership of fcdbd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSoF../8c57c.. ownership of f52fd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLUD../c5a1e.. ownership of 4fc0a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWTQ../ea672.. ownership of ab832.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNSe../cd396.. ownership of acdac.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUGX../5eb5c.. ownership of bebf6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU5Q../268dd.. ownership of bd60a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEq8../b115a.. ownership of 5d578.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWLW../a4715.. ownership of 2c950.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMScx../a51d3.. ownership of 64ca8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH7r../1a34e.. ownership of 619c0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQvr../19515.. ownership of c9ba2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZMz../acb54.. ownership of 9b05e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVED../9b6f4.. ownership of 783bc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbWX../31220.. ownership of cf954.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUYBj../d6393.. 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 eb53d.. : ι → CT2 ι
Param 1216a.. : ι → (ι → ο) → ι
Definition 783bc.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 x4 : ι → ο . 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) (1216a.. x0 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 0edec.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = 783bc.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem e1561.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . x0 = f482f.. (783bc.. 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 ec944.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = 783bc.. 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 6ffdb.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (783bc.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Param e3162.. : ι → ι → ι → ι
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 35054.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ e3162.. (eb53d.. x0 x1) x2 x3 = x1 x2 x3
Theorem 1d7a9.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = 783bc.. 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 8844f.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (783bc.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Param decode_p : ι → ι → ο
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
Known 931fe.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . prim1 x2 x0 ⟶ decode_p (1216a.. x0 x1) x2 = x1 x2
Theorem e347f.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = 783bc.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 46d59.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (783bc.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (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 77353.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = 783bc.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 6944d.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (783bc.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (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 b1e5b.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 x8 x9 : ι → ο . 783bc.. x0 x2 x4 x6 x8 = 783bc.. 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10)) (∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10) (proof)
Param iff : ο → ο → ο
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Known 8fdaf.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = x2 x3 x4) ⟶ eb53d.. x0 x1 = eb53d.. x0 x2
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 a7310.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 x7 x8 : ι → ο . (∀ x9 : ι → ο . (∀ x10 . x9 x10 ⟶ prim1 x10 x0) ⟶ iff (x1 x9) (x2 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x3 x9 x10 = x4 x9 x10) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x5 x9) (x6 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ 783bc.. x0 x1 x3 x5 x7 = 783bc.. x0 x2 x4 x6 x8 (proof)
Definition c9ba2.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 x6 : ι → ο . x1 (783bc.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 4344e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 x4 : ι → ο . c9ba2.. (783bc.. x0 x1 x2 x3 x4) (proof)
Theorem 0d70c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . c9ba2.. (783bc.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 75cc6.. : ∀ x0 . c9ba2.. x0 ⟶ x0 = 783bc.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 64ca8.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 7046d.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 64ca8.. (783bc.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 5d578.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 3a7bb.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 5d578.. (783bc.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition bebf6.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 : ι → ο . λ 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) x4))))
Theorem e31dc.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = bebf6.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 4d890.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = f482f.. (bebf6.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 6bf38.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = bebf6.. 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 2f459.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (bebf6.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 8d565.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = bebf6.. 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 546c0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (bebf6.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem c5e5b.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = bebf6.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem bedba.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (bebf6.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem afc32.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = bebf6.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 7bb35.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x4 = f482f.. (bebf6.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 4f115.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ο . ∀ x8 x9 . bebf6.. x0 x2 x4 x6 x8 = bebf6.. 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ x6 x10 = x7 x10)) (x8 = x9) (proof)
Theorem d3e57.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ο . ∀ x7 . (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ iff (x1 x8) (x2 x8)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x8 x9 = x4 x8 x9) ⟶ (∀ x8 . prim1 x8 x0 ⟶ iff (x5 x8) (x6 x8)) ⟶ bebf6.. x0 x1 x3 x5 x7 = bebf6.. x0 x2 x4 x6 x7 (proof)
Definition ab832.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 : ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (bebf6.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 18431.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ab832.. (bebf6.. x0 x1 x2 x3 x4) (proof)
Theorem 04af0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . ab832.. (bebf6.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem a85d0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . ab832.. (bebf6.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 5da3a.. : ∀ x0 . ab832.. x0 ⟶ x0 = bebf6.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition f52fd.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem d409f.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ f52fd.. (bebf6.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 971dc.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 13766.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 971dc.. (bebf6.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 6b0a5.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . 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..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))
Theorem 3c3d8.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . x0 = 6b0a5.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 4bb01.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . x0 = f482f.. (6b0a5.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 96968.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . x0 = 6b0a5.. 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 cd382.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (6b0a5.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem b21e7.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . x0 = 6b0a5.. 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 1c594.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (6b0a5.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 8d5fd.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . x0 = 6b0a5.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem c7eb2.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . x3 = f482f.. (6b0a5.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 56b62.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . x0 = 6b0a5.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 5753b.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . x4 = f482f.. (6b0a5.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 24d22.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 x8 x9 . 6b0a5.. x0 x2 x4 x6 x8 = 6b0a5.. 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 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (x6 = x7)) (x8 = x9) (proof)
Theorem a72a6.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x0) ⟶ iff (x1 x7) (x2 x7)) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x3 x7 x8 = x4 x7 x8) ⟶ 6b0a5.. x0 x1 x3 x5 x6 = 6b0a5.. x0 x2 x4 x5 x6 (proof)
Definition 8b540.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (6b0a5.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 08cf8.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 8b540.. (6b0a5.. x0 x1 x2 x3 x4) (proof)
Theorem da0e2.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . 8b540.. (6b0a5.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem 402fa.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . 8b540.. (6b0a5.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 6c39d.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . 8b540.. (6b0a5.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem ae43e.. : ∀ x0 . 8b540.. x0 ⟶ x0 = 6b0a5.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition d0646.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 5ba00.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ d0646.. (6b0a5.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 3b3d8.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 1eb75.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 x5 . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι → ι . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ x3 x8 x9 = x7 x8 x9) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 3b3d8.. (6b0a5.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition 34992.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι . λ x3 x4 : ι → ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (λ x5 . If_i (x5 = 4a7ef..) x0 (If_i (x5 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) (d2155.. x0 x4)))))
Theorem 6998e.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 34992.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem af941.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 x5 : ι → ι → ο . x5 x0 (f482f.. (34992.. x0 x1 x2 x3 x4) 4a7ef..) ⟶ x5 (f482f.. (34992.. x0 x1 x2 x3 x4) 4a7ef..) x0 (proof)
Theorem 9c9ff.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 34992.. 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 0a284.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (34992.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 6d328.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 34992.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 0f0c4.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (34992.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Param 2b2e3.. : ι → ι → ι → ο
Known 67416.. : ∀ x0 . ∀ x1 : ι → ι → ο . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ 2b2e3.. (d2155.. x0 x1) x2 x3 = x1 x2 x3
Theorem 7173f.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 34992.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x4 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 x7 (proof)
Theorem fa07e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (34992.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem bcf71.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = 34992.. 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 c22ae.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x4 x5 x6 = 2b2e3.. (f482f.. (34992.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 x6 (proof)
Theorem c0c2b.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . ∀ x6 x7 x8 x9 : ι → ι → ο . 34992.. x0 x2 x4 x6 x8 = 34992.. 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)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x6 x10 x11 = x7 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x8 x10 x11 = x9 x10 x11) (proof)
Known 62ef7.. : ∀ x0 . ∀ x1 x2 : ι → ι → ο . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ iff (x1 x3 x4) (x2 x3 x4)) ⟶ d2155.. x0 x1 = d2155.. x0 x2
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Theorem 2f911.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι . ∀ x5 x6 x7 x8 : ι → ι → ο . (∀ x9 : ι → ο . (∀ x10 . x9 x10 ⟶ prim1 x10 x0) ⟶ iff (x1 x9) (x2 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ x3 x9 = x4 x9) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x5 x9 x10) (x6 x9 x10)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ iff (x7 x9 x10) (x8 x9 x10)) ⟶ 34992.. x0 x1 x3 x5 x7 = 34992.. x0 x2 x4 x6 x8 (proof)
Definition 49161.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 x6 : ι → ι → ο . x1 (34992.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 30c66.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 x4 : ι → ι → ο . 49161.. (34992.. x0 x1 x2 x3 x4) (proof)
Theorem 58b23.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . 49161.. (34992.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem 3f026.. : ∀ x0 . 49161.. x0 ⟶ x0 = 34992.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition cd973.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 9e0ff.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ ∀ x9 : ι → ι → ο . (∀ x10 . prim1 x10 x1 ⟶ ∀ x11 . prim1 x11 x1 ⟶ iff (x5 x10 x11) (x9 x10 x11)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ cd973.. (34992.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 0d56c.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem caeb2.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : (ι → ο) → ο . (∀ x7 : ι → ο . (∀ x8 . x7 x8 ⟶ prim1 x8 x1) ⟶ iff (x2 x7) (x6 x7)) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ x8 : ι → ι → ο . (∀ x9 . prim1 x9 x1 ⟶ ∀ x10 . prim1 x10 x1 ⟶ iff (x4 x9 x10) (x8 x9 x10)) ⟶ ∀ x9 : ι → ι → ο . (∀ x10 . prim1 x10 x1 ⟶ ∀ x11 . prim1 x11 x1 ⟶ iff (x5 x10 x11) (x9 x10 x11)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 0d56c.. (34992.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)