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Proofgold Signed Transaction

vin
PrGNF../05a36..
PUX8C../3e284..
vout
PrGNF../e8265.. 24.98 bars
TMKsg../c99fe.. ownership of 3db9b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKrm../dcbd8.. ownership of 089e8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa8j../a56c4.. ownership of 7d0b3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFTm../3e156.. ownership of 10493.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVju../2e73c.. ownership of 1c1fb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPdn../4cd01.. ownership of 8051f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUEi../9c9f7.. ownership of 59c4d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTdH../4a8a4.. ownership of eb2ef.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZEo../2e656.. ownership of 5a473.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUWi../3be6c.. ownership of 4b0f6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZYT../33957.. ownership of c905c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZKk../d0627.. ownership of e2b66.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKDo../13e6b.. ownership of 02f07.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJw7../7ef91.. ownership of 9c2e2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVvM../98c78.. ownership of 0f819.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU18../bcf8c.. ownership of 99828.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQA7../bd497.. ownership of 67814.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWE1../aedd2.. ownership of 3ab78.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLFT../d22c9.. ownership of 846b3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYVd../4205d.. ownership of 31c41.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKav../0250a.. ownership of 9b6e5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcJ6../fb174.. ownership of 04e91.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK4H../7607a.. ownership of 528c2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWPz../ee676.. ownership of 02db6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPHV../c5d74.. ownership of dc308.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZbf../401c6.. ownership of 08751.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNVF../8aa38.. ownership of dbbce.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR6k../80984.. ownership of b2ef2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdVQ../d36a8.. ownership of 071f5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQk6../540b7.. ownership of a13b3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUKy../c6191.. ownership of 7075a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ2H../93bac.. ownership of 9eaa9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLzv../0022b.. ownership of f77a7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRZg../f184d.. ownership of 5091b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMwz../120a1.. ownership of acfd5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLyn../25b19.. ownership of f50dd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKHn../e8544.. ownership of be7e4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRgs../f86a5.. ownership of d2a9d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbff../211ca.. ownership of 63a8c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWjn../f8806.. ownership of 8b11b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRka../97b67.. ownership of b1dc2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZBQ../de068.. ownership of df397.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRvc../eada5.. ownership of 819e3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEnh../99c7f.. ownership of 8f422.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVJL../33521.. ownership of 70513.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML9k../65592.. ownership of b2fda.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSN8../af532.. ownership of f74bd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdye../2b7f1.. ownership of bed96.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQJo../bef3e.. ownership of c1ea6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXis../dac7a.. ownership of 313a6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJzt../9bdfc.. ownership of 58f90.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUrn../c6ad3.. ownership of 1c902.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQjC../f007f.. ownership of 298cb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdDv../bc8ff.. ownership of 85802.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFri../5a503.. ownership of c4d00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcmh../1f033.. ownership of 0aba2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJiK../4ba4d.. ownership of a66f2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdzG../58af0.. ownership of 2cd10.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHRh../52bc3.. ownership of 95606.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXMG../53b47.. ownership of 5e1f7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYpW../24933.. ownership of 5ca46.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHUA../6cdbe.. ownership of 85397.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYpa../f2bd8.. ownership of 5fca6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGoc../8bc57.. ownership of e7682.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUPq../b7f38.. ownership of 9e061.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLDf../b9c93.. ownership of 3da02.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQdK../62de7.. ownership of a0755.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbqr../9f6c9.. ownership of ae678.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMafT../956ea.. ownership of 7c086.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ4A../7a978.. ownership of 8f7e1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHau../d927d.. ownership of 1c3a3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVBk../ee4e0.. ownership of 39341.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbVx../e78d2.. ownership of 4f310.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ4V../881f7.. ownership of 8ec7e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY2E../c8ce6.. ownership of e13bf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXcT../88c15.. ownership of bc999.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK5c../96a45.. ownership of e9780.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQmT../25784.. ownership of 7ad92.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPL4../46172.. ownership of 82387.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRwk../2f0ec.. ownership of ea50b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMn1../44658.. ownership of e6954.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRnW../02782.. ownership of d98ac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPKA../1063f.. ownership of dc4c2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLBH../7426e.. ownership of 7316e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWXc../b6e0a.. ownership of 3ce02.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPJD../0c3eb.. ownership of 00960.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYFr../8c446.. ownership of bf20a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPGw../fa08b.. ownership of 514c1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG6u../d121e.. ownership of c359b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYKW../6edd3.. ownership of ff141.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMahA../83706.. ownership of 24e08.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGtf../1b63b.. ownership of c2dfa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML2p../a24f6.. ownership of 1e09f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJCA../9e772.. ownership of 9f179.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKT6../09aaf.. ownership of 1b0ab.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXgX../c41a1.. ownership of df433.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMCj../c05e3.. ownership of 97f65.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHN8../0a10e.. ownership of 20303.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLG7../1e886.. ownership of fd38c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT6n../a6fa2.. ownership of e7fb1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbUe../18f5d.. ownership of 60346.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXqx../f0d17.. ownership of c7f8d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRTE../6dca0.. ownership of aa832.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGYh../95060.. ownership of 76b5a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN5e../bdc50.. ownership of d8071.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdWp../b975e.. ownership of 926f5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGzy../87f93.. ownership of 651a8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRoo../0a607.. ownership of 17c3f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNng../a405c.. ownership of a36e4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWWn../6afda.. ownership of a877a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUa7../c1d43.. ownership of 3735e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNLP../d454a.. ownership of 8c18b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbJv../7bbb1.. ownership of 6dc05.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWrD../eaf31.. ownership of 1caf0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYVU../10e90.. ownership of 8bc32.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPm1../f9e5e.. ownership of d32b9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWu3../8120e.. ownership of 924a0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKEV../0ea38.. ownership of 6e7ef.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPqo../14f89.. ownership of 0facc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdmq../dcb9e.. ownership of 9eb03.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX9F../d424b.. ownership of 3cd86.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUsH../4055c.. ownership of 3ae4f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVqJ../0c1cf.. ownership of 87375.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXzg../b1e77.. ownership of 403b9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdZv../71148.. ownership of 627d4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb5P../4dc13.. ownership of d1c17.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNF4../db5fe.. ownership of cc9d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXXR../65669.. ownership of b3e4d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN86../c99c5.. ownership of 41de0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFy1../c6252.. ownership of 4fc33.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT7r../7acde.. ownership of b554d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLMj../5470b.. ownership of ee4e9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY4L../4adc2.. ownership of 84fcd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGPX../187d8.. ownership of 76e35.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU6P../32315.. ownership of 9e1cf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTPQ../e2d50.. ownership of 63955.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVPr../7823a.. ownership of 4b222.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbng../38e9a.. ownership of a1b93.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKhy../0a988.. ownership of 8208e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPZn../7e020.. ownership of f98fc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNkw../a48f8.. ownership of 5592c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPc3../76622.. ownership of 98c63.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdRi../50132.. ownership of 2def8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF1Y../4a9f0.. ownership of bab04.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKVS../36959.. ownership of 0670d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXDY../3ae91.. ownership of d1dfc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbe5../b77c8.. ownership of 2e40c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNJE../6163c.. ownership of 5be97.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYkm../db26d.. ownership of 08fa6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVsU../d6c78.. ownership of 68ca3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZbh../91896.. ownership of 16885.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYe1../3d52c.. ownership of 5221c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG7G../b88dd.. ownership of 24ba9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSS3../6c700.. ownership of f1581.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZhr../d8bde.. ownership of f4fb4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXVb../cf2d3.. ownership of 7ea11.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZkH../db8f4.. ownership of 85724.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFkk../bb849.. ownership of 071e7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ3G../5a4e3.. ownership of 3259d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXEq../5cd19.. ownership of a8cdf.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJna../1e302.. ownership of d4af0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSLi../e03b8.. ownership of c38bc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXqg../a1da3.. ownership of 608f4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHaK../4411a.. ownership of fee0b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQTo../465e0.. ownership of 27e22.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFut../321bd.. ownership of f4fb5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZgB../479ac.. ownership of cf688.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbXp../23ca4.. ownership of 0017a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWYH../ce3b8.. ownership of 687c3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVL4../ceb1a.. ownership of 291b2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG3X../326a1.. ownership of 7ac32.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLuW../b676f.. ownership of a5af8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUR3i../6666c.. 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 d2155.. : ι → (ι → ι → ο) → ι
Param 1216a.. : ι → (ι → ο) → ι
Definition 7ac32.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι . λ x3 : ι → ι → ο . λ 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..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. 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 8208e.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 7ac32.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 4b222.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . x0 = f482f.. (7ac32.. 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 9e1cf.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 7ac32.. 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 84fcd.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (7ac32.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
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 f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem b554d.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 7ac32.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 41de0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (7ac32.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Param 2b2e3.. : ι → 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 67416.. : ∀ x0 . ∀ x1 : ι → ι → ο . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ 2b2e3.. (d2155.. x0 x1) x2 x3 = x1 x2 x3
Theorem cc9d8.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 7ac32.. 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 627d4.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (7ac32.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Param decode_p : ι → ι → ο
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
Known 931fe.. : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . prim1 x2 x0 ⟶ decode_p (1216a.. x0 x1) x2 = x1 x2
Theorem 87375.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . x0 = 7ac32.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 3cd86.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (7ac32.. 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 0facc.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 : ι → ο . 7ac32.. x0 x2 x4 x6 x8 = 7ac32.. 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 ⟶ 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 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
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 924a0.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι . ∀ x5 x6 : ι → ι → ο . ∀ x7 x8 : 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 ⟶ iff (x7 x9) (x8 x9)) ⟶ 7ac32.. x0 x1 x3 x5 x7 = 7ac32.. x0 x2 x4 x6 x8 (proof)
Definition 687c3.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ι → ο . ∀ x6 : ι → ο . x1 (7ac32.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 8bc32.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 687c3.. (7ac32.. x0 x1 x2 x3 x4) (proof)
Theorem 6dc05.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . 687c3.. (7ac32.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 3735e.. : ∀ x0 . 687c3.. x0 ⟶ x0 = 7ac32.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition cf688.. := 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..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem a36e4.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : 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 → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ cf688.. (7ac32.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 27e22.. := 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..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 651a8.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 : 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 → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5) ⟶ 27e22.. (7ac32.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 608f4.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι . λ x3 : ι → 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..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (d2155.. x0 x3) x4))))
Theorem d8071.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 608f4.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem aa832.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x0 = f482f.. (608f4.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 60346.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 608f4.. 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 fd38c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (608f4.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 97f65.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 608f4.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 1b0ab.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (608f4.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 1e09f.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 608f4.. 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 24e08.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (608f4.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem c359b.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . x0 = 608f4.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem bf20a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . x4 = f482f.. (608f4.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 3ce02.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . ∀ x6 x7 : ι → ι → ο . ∀ x8 x9 . 608f4.. x0 x2 x4 x6 x8 = 608f4.. 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)) (x8 = x9) (proof)
Theorem dc4c2.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι . ∀ x5 x6 : ι → ι → ο . ∀ x7 . (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ iff (x1 x8) (x2 x8)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ x3 x8 = x4 x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ iff (x5 x8 x9) (x6 x8 x9)) ⟶ 608f4.. x0 x1 x3 x5 x7 = 608f4.. x0 x2 x4 x6 x7 (proof)
Definition d4af0.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (608f4.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem e6954.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ d4af0.. (608f4.. x0 x1 x2 x3 x4) (proof)
Theorem 82387.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . d4af0.. (608f4.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem e9780.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . d4af0.. (608f4.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem e13bf.. : ∀ x0 . d4af0.. x0 ⟶ x0 = 608f4.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 3259d.. := 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..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 4f310.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . (∀ 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)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 3259d.. (608f4.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 85724.. := 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..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 1c3a3.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ι → ο) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ι → ο . ∀ x5 . (∀ 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)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 85724.. (608f4.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition f4fb4.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : 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..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) (1216a.. x0 x4)))))
Theorem 7c086.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ο . x0 = f4fb4.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem a0755.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ο . x0 = f482f.. (f4fb4.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 9e061.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ο . x0 = f4fb4.. 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 5fca6.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (f4fb4.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 5ca46.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ο . x0 = f4fb4.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 95606.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (f4fb4.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem a66f2.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ο . x0 = f4fb4.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem c4d00.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (f4fb4.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 298cb.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ο . x0 = f4fb4.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 58f90.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (f4fb4.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem c1ea6.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . ∀ x6 x7 x8 x9 : ι → ο . f4fb4.. x0 x2 x4 x6 x8 = f4fb4.. 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 ⟶ x6 x10 = x7 x10)) (∀ x10 . prim1 x10 x0 ⟶ x8 x10 = x9 x10) (proof)
Theorem f74bd.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : 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 ⟶ x3 x9 = x4 x9) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x5 x9) (x6 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ f4fb4.. x0 x1 x3 x5 x7 = f4fb4.. x0 x2 x4 x6 x8 (proof)
Definition 24ba9.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 x6 : ι → ο . x1 (f4fb4.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 70513.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 x4 : ι → ο . 24ba9.. (f4fb4.. x0 x1 x2 x3 x4) (proof)
Theorem 819e3.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ο . 24ba9.. (f4fb4.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem b1dc2.. : ∀ x0 . 24ba9.. x0 ⟶ x0 = f4fb4.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition 16885.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem 63a8c.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : 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 . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 16885.. (f4fb4.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 08fa6.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem be7e4.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : 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 . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ 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) ⟶ 08fa6.. (f4fb4.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 2e40c.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : 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..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) x4))))
Theorem acfd5.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 2e40c.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem f77a7.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = f482f.. (2e40c.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 7075a.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 2e40c.. 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 071f5.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x0) ⟶ x1 x5 = decode_c (f482f.. (2e40c.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 (proof)
Theorem dbbce.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 2e40c.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem dc308.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (2e40c.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
Theorem 528c2.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 2e40c.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 9b6e5.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (2e40c.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 846b3.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 2e40c.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 67814.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . x4 = f482f.. (2e40c.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 0f819.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι . ∀ x6 x7 : ι → ο . ∀ x8 x9 . 2e40c.. x0 x2 x4 x6 x8 = 2e40c.. 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 ⟶ x6 x10 = x7 x10)) (x8 = x9) (proof)
Theorem 02f07.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : 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 ⟶ x3 x8 = x4 x8) ⟶ (∀ x8 . prim1 x8 x0 ⟶ iff (x5 x8) (x6 x8)) ⟶ 2e40c.. x0 x1 x3 x5 x7 = 2e40c.. x0 x2 x4 x6 x7 (proof)
Definition 0670d.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 : ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (2e40c.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem c905c.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ 0670d.. (2e40c.. x0 x1 x2 x3 x4) (proof)
Theorem 5a473.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . 0670d.. (2e40c.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem 59c4d.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι . ∀ x3 : ι → ο . ∀ x4 . 0670d.. (2e40c.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 1c1fb.. : ∀ x0 . 0670d.. x0 ⟶ x0 = 2e40c.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 2def8.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 7d0b3.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : 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 . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 2def8.. (2e40c.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 5592c.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 3db9b.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι) → (ι → ο) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : 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 . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ x0 x1 x6 x7 x8 x5 = x0 x1 x2 x3 x4 x5) ⟶ 5592c.. (2e40c.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)