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Proofgold Signed Transaction

vin
PrAmQ../1a956..
PUWvp../8826a..
vout
PrAmQ../d8c52.. 9.95 bars
TMW2t../c7c2f.. ownership of 16888.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT9n../2d8d5.. ownership of 674ca.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJ3P../9808d.. ownership of 720ab.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa97../b7081.. ownership of 91e98.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPRs../21876.. ownership of 4e54b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMnU../e88a4.. ownership of e4896.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMuC../1303e.. ownership of e8b51.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM29../5a1fe.. ownership of d7ce8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPEK../b354c.. ownership of b2f98.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGZF../15584.. ownership of 1c768.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMwi../3ec25.. ownership of 81997.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdk5../9aea7.. ownership of 5c7dc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVhU../7eba1.. ownership of 091be.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSDK../68163.. ownership of b2742.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJmU../43113.. ownership of eedd2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY1K../ca9b4.. ownership of 1e401.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMddh../873c3.. ownership of b7c93.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYuu../f5234.. ownership of 461a5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdjw../8133d.. ownership of c24d1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTtW../1ff50.. ownership of 5e6d4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLNE../6be47.. ownership of e9d56.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPLo../bd41f.. ownership of 11a43.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPx8../2d3b4.. ownership of c4fff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJZt../a3fd2.. ownership of 5e493.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJak../617bd.. ownership of 27a5d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUYd../25fa8.. ownership of 87bcd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFyj../161d6.. ownership of 0ec69.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUXM../7da4e.. ownership of 6353d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGrE../9c2de.. ownership of 64d90.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFYw../d99a1.. ownership of 0e532.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN8c../b1e85.. ownership of c83d9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTm8../09741.. ownership of 3d18c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK1H../e346d.. ownership of 2e953.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTV3../f3335.. ownership of 17398.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKo3../64eff.. ownership of 180e1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJSp../b78d2.. ownership of 29e22.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ84../8d5c1.. ownership of 35a92.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcLb../d8a25.. ownership of 7df10.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLVC../82385.. ownership of deafe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbjr../1dadf.. ownership of 66c12.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPe6../d3024.. ownership of 73971.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGpf../9985d.. ownership of 77ee0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRSV../201bb.. ownership of b3cb1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEnM../a889b.. ownership of bace2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKPU../1e84d.. ownership of bd187.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUgD../5a25a.. ownership of ba149.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFx7../be53f.. ownership of 8b266.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXZJ../6d9c4.. ownership of b00f9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUq6../5d08c.. ownership of e2026.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU67../356a1.. ownership of 08d0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbhL../c44ce.. ownership of e5de9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF5t../a999c.. ownership of da539.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTNT../68bc6.. ownership of 6c7ce.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa6N../7fb0e.. ownership of ef9e8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGn2../d4b2a.. ownership of a0c42.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTXr../d86ba.. ownership of 7b768.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa23../612d3.. ownership of b6ec5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMStC../000aa.. ownership of 90705.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFym../d39c0.. ownership of fd9e5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVRU../6021a.. ownership of ba81b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSQ7../e2b31.. ownership of 25248.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTrU../f1843.. ownership of 3be47.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN3K../72df7.. ownership of 9dc85.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMErL../8bf47.. ownership of 462b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQZN../8653a.. ownership of 4fdde.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSDd../bcdbf.. ownership of f495c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFH3../acb87.. ownership of 29de5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFkW../907da.. ownership of 78e50.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKdC../47bef.. ownership of 36ae3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcyW../2666f.. ownership of 25464.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbgZ../2197f.. ownership of be87a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLLA../7a85e.. ownership of b3a12.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRvG../b6610.. ownership of db71d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKjR../1892e.. ownership of 5ef07.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPT5../8587f.. ownership of dc2a8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML64../3bd2a.. ownership of 1fd6f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV9y../11293.. ownership of d0243.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWuB../6158f.. ownership of d6b44.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWcA../cd3ee.. ownership of 3dc96.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc1G../d40fd.. ownership of 3b715.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTHn../82928.. ownership of eac17.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZBU../9a0db.. ownership of da8ba.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdiu../07394.. ownership of f7540.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYT6../a28b4.. ownership of 8fa66.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWJ9../58393.. ownership of db256.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPEB../fcf6e.. ownership of f13df.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZSM../9a20e.. ownership of 40117.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLfv../44a5f.. ownership of 1624c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRVM../7e6fb.. ownership of 39c7e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUpD../68764.. ownership of 56935.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV64../8b96e.. ownership of 6b3af.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYJq../fdf2e.. ownership of b6305.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYxD../ad965.. ownership of 9aeec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ38../4868b.. ownership of a7a67.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXms../4d374.. ownership of 17011.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJRL../eefbe.. ownership of 49305.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQhf../da299.. ownership of 6bc8d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNsE../9aee6.. ownership of 6a52b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK1x../99e56.. ownership of 349ee.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWcM../d50c1.. ownership of daede.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYTq../25359.. ownership of 22793.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUGM../756c7.. ownership of 79caf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKRV../46609.. ownership of 8b6c0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNRJ../f9f42.. ownership of 18c6a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPmW../7f905.. ownership of 0ebe9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJMd../99604.. ownership of 8ac77.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY6z../02a5e.. ownership of 54839.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVMw../0c4f1.. ownership of 5e5d3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdkS../c441c.. ownership of d4012.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUj9../8b87c.. ownership of 3a77e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH7z../09a37.. ownership of 4695f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTkD../c6d63.. ownership of e86de.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSMD../a2945.. ownership of e0fb6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW9B../c6e62.. ownership of e6864.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFwW../9c661.. ownership of 43599.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHh8../e14ea.. ownership of 16c37.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEge../9c4fa.. ownership of 680a0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYbd../9d4e0.. ownership of c9eab.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMb5../a1e92.. ownership of d044c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKyK../fcb0b.. ownership of 92111.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdpC../6f28e.. ownership of 370e3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGKF../73635.. ownership of f9841.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJj9../ecb75.. ownership of 55ff1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa5c../46ef1.. ownership of 70c4d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ8Y../31599.. ownership of 43515.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaGf../ef9bc.. ownership of 79667.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYSa../defd6.. ownership of ac2cd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbfB../24b9c.. ownership of 903b4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaWa../d3f0e.. ownership of 0a1fb.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXFr../94d6c.. ownership of 66db3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPz6../582c0.. ownership of e8b89.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPXn../32959.. ownership of 818b3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN72../b46f2.. ownership of 80b53.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLfQ../f03eb.. ownership of 13160.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ5y../e184a.. ownership of 75035.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdWU../09f36.. ownership of 54d76.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJJu../c8c86.. ownership of d7d76.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK9v../6c81a.. ownership of 22d9d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGkV../18526.. ownership of d7d7e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWLM../37a2f.. ownership of e8c04.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXnU../cfc9c.. ownership of 9e417.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKY6../b98d7.. ownership of 97bea.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXAW../971ad.. ownership of 357b4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVoS../c47a3.. ownership of 6744c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX1X../51bda.. ownership of 9ec2e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVkb../064e5.. ownership of 006a8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbse../e1afe.. ownership of dd9fd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKjb../8b689.. ownership of 35b2a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdYd../25949.. ownership of bc70e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXkJ../46f85.. ownership of 8bacc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVCT../39c9e.. ownership of 2d48d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQj3../139b2.. ownership of d67fd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZaw../7fe4e.. ownership of 0df03.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUaX../eeac7.. ownership of 0d7d4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJfs../668b7.. ownership of 21805.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSDR../fc008.. ownership of f68e3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUPwT../dde04.. 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
Definition 21805.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 : ι → ι . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) (0fc90.. x0 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 55ff1.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . x0 = 21805.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 370e3.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . x0 = f482f.. (21805.. x0 x1 x2 x3) 4a7ef.. (proof)
Param decode_c : ι → (ι → ο) → ο
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 81500.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ο . (∀ x3 . x2 x3 ⟶ prim1 x3 x0) ⟶ decode_c (e0e40.. x0 x1) x2 = x1 x2
Theorem d044c.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . x0 = 21805.. x1 x2 x3 x4 ⟶ ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ x2 x5 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 680a0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x0) ⟶ x1 x4 = decode_c (f482f.. (21805.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Param e3162.. : ι → ι → ι → ι
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 35054.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ e3162.. (eb53d.. x0 x1) x2 x3 = x1 x2 x3
Theorem 43599.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . x0 = 21805.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem e0fb6.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = e3162.. (f482f.. (21805.. 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
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 4695f.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . x0 = 21805.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x4 x5 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem d4012.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 . prim1 x4 x0 ⟶ x3 x4 = f482f.. (f482f.. (21805.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (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 54839.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ι . 21805.. x0 x2 x4 x6 = 21805.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8) (proof)
Param iff : ο → ο → ο
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
Known 8fdaf.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ x1 x3 x4 = x2 x3 x4) ⟶ eb53d.. x0 x1 = eb53d.. x0 x2
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 0ebe9.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ι . (∀ 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) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x5 x7 = x6 x7) ⟶ 21805.. x0 x1 x3 x5 = 21805.. x0 x2 x4 x6 (proof)
Definition 0df03.. := 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 → ι . (∀ x6 . prim1 x6 x2 ⟶ prim1 (x5 x6) x2) ⟶ x1 (21805.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 8b6c0.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ι . (∀ x4 . prim1 x4 x0 ⟶ prim1 (x3 x4) x0) ⟶ 0df03.. (21805.. x0 x1 x2 x3) (proof)
Theorem 22793.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . 0df03.. (21805.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x4 x5) x0 (proof)
Theorem 349ee.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . 0df03.. (21805.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x3 x4) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 6bc8d.. : ∀ x0 . 0df03.. x0 ⟶ x0 = 21805.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 2d48d.. := 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.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 17011.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x4 x8 = x7 x8) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ 2d48d.. (21805.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition bc70e.. := 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.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 9aeec.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι . (∀ x8 . prim1 x8 x1 ⟶ x4 x8 = x7 x8) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ bc70e.. (21805.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition dd9fd.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → 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..) (e0e40.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) (d2155.. x0 x3))))
Theorem 6b3af.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . x0 = dd9fd.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 39c7e.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . x4 x0 (f482f.. (dd9fd.. x0 x1 x2 x3) 4a7ef..) ⟶ x4 (f482f.. (dd9fd.. x0 x1 x2 x3) 4a7ef..) x0 (proof)
Theorem 40117.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . x0 = dd9fd.. x1 x2 x3 x4 ⟶ ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ x2 x5 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem db256.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x0) ⟶ x1 x4 = decode_c (f482f.. (dd9fd.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Theorem f7540.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . x0 = dd9fd.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem eac17.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = e3162.. (f482f.. (dd9fd.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 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 3dc96.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . x0 = dd9fd.. 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 d0243.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x3 x4 x5 = 2b2e3.. (f482f.. (dd9fd.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 x5 (proof)
Theorem dc2a8.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ι → ο . dd9fd.. x0 x2 x4 x6 = dd9fd.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x6 x8 x9 = x7 x8 x9) (proof)
Known 62ef7.. : ∀ x0 . ∀ x1 x2 : ι → ι → ο . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ iff (x1 x3 x4) (x2 x3 x4)) ⟶ d2155.. x0 x1 = d2155.. x0 x2
Theorem db71d.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ι → ο . (∀ 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) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (x5 x7 x8) (x6 x7 x8)) ⟶ dd9fd.. x0 x1 x3 x5 = dd9fd.. x0 x2 x4 x6 (proof)
Definition 9ec2e.. := 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 → ι → ο . x1 (dd9fd.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem be87a.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ι → ο . 9ec2e.. (dd9fd.. x0 x1 x2 x3) (proof)
Theorem 36ae3.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . 9ec2e.. (dd9fd.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x4 x5) x0 (proof)
Theorem 29de5.. : ∀ x0 . 9ec2e.. x0 ⟶ x0 = dd9fd.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 357b4.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 4fdde.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 357b4.. (dd9fd.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 9e417.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 9dc85.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ι → ο . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 9e417.. (dd9fd.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Param 1216a.. : ι → (ι → ο) → ι
Definition d7d7e.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 : ι → ο . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) (1216a.. x0 x3))))
Theorem 25248.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . x0 = d7d7e.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem fd9e5.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . x0 = f482f.. (d7d7e.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem b6ec5.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . x0 = d7d7e.. x1 x2 x3 x4 ⟶ ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ x2 x5 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem a0c42.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x0) ⟶ x1 x4 = decode_c (f482f.. (d7d7e.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Theorem 6c7ce.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . x0 = d7d7e.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem e5de9.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = e3162.. (f482f.. (d7d7e.. x0 x1 x2 x3) (4ae4a.. (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 e2026.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . x0 = d7d7e.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x4 x5 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 8b266.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ x3 x4 = decode_p (f482f.. (d7d7e.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (proof)
Theorem bd187.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ο . d7d7e.. x0 x2 x4 x6 = d7d7e.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9)) (∀ x8 . prim1 x8 x0 ⟶ x6 x8 = x7 x8) (proof)
Known ee7ef.. : ∀ x0 . ∀ x1 x2 : ι → ο . (∀ x3 . prim1 x3 x0 ⟶ iff (x1 x3) (x2 x3)) ⟶ 1216a.. x0 x1 = 1216a.. x0 x2
Theorem b3cb1.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ο . (∀ 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) ⟶ (∀ x7 . prim1 x7 x0 ⟶ iff (x5 x7) (x6 x7)) ⟶ d7d7e.. x0 x1 x3 x5 = d7d7e.. x0 x2 x4 x6 (proof)
Definition d7d76.. := 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 . x1 (d7d7e.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 73971.. : ∀ 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 . d7d76.. (d7d7e.. x0 x1 x2 x3) (proof)
Theorem deafe.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ο . d7d76.. (d7d7e.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x4 x5) x0 (proof)
Theorem 35a92.. : ∀ x0 . d7d76.. x0 ⟶ x0 = d7d7e.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 75035.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (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..)))))
Theorem 180e1.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ 75035.. (d7d7e.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 80b53.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (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..)))))
Theorem 2e953.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → (ι → ο) → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 : ι → ο . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4) ⟶ 80b53.. (d7d7e.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition e8b89.. := λ x0 . λ x1 : (ι → ο) → ο . λ x2 : ι → ι → ι . λ x3 . 0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (λ x4 . If_i (x4 = 4a7ef..) x0 (If_i (x4 = 4ae4a.. 4a7ef..) (e0e40.. x0 x1) (If_i (x4 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) x3)))
Theorem c83d9.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 . x0 = e8b89.. x1 x2 x3 x4 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 64d90.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 . x0 = f482f.. (e8b89.. x0 x1 x2 x3) 4a7ef.. (proof)
Theorem 0ec69.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 . x0 = e8b89.. x1 x2 x3 x4 ⟶ ∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ x2 x5 = decode_c (f482f.. x0 (4ae4a.. 4a7ef..)) x5 (proof)
Theorem 27a5d.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 . ∀ x4 : ι → ο . (∀ x5 . x4 x5 ⟶ prim1 x5 x0) ⟶ x1 x4 = decode_c (f482f.. (e8b89.. x0 x1 x2 x3) (4ae4a.. 4a7ef..)) x4 (proof)
Theorem c4fff.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 . x0 = e8b89.. x1 x2 x3 x4 ⟶ ∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x5 x6 = e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem e9d56.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ x2 x4 x5 = e3162.. (f482f.. (e8b89.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) x4 x5 (proof)
Theorem c24d1.. : ∀ x0 x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 . x0 = e8b89.. x1 x2 x3 x4 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem b7c93.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 . x3 = f482f.. (e8b89.. x0 x1 x2 x3) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem eedd2.. : ∀ x0 x1 . ∀ x2 x3 : (ι → ο) → ο . ∀ x4 x5 : ι → ι → ι . ∀ x6 x7 . e8b89.. x0 x2 x4 x6 = e8b89.. x1 x3 x5 x7 ⟶ and (and (and (x0 = x1) (∀ x8 : ι → ο . (∀ x9 . x8 x9 ⟶ prim1 x9 x0) ⟶ x2 x8 = x3 x8)) (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x4 x8 x9 = x5 x8 x9)) (x6 = x7) (proof)
Theorem 091be.. : ∀ x0 . ∀ x1 x2 : (ι → ο) → ο . ∀ x3 x4 : ι → ι → ι . ∀ x5 . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x0) ⟶ iff (x1 x6) (x2 x6)) ⟶ (∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x3 x6 x7 = x4 x6 x7) ⟶ e8b89.. x0 x1 x3 x5 = e8b89.. x0 x2 x4 x5 (proof)
Definition 0a1fb.. := 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 ⟶ x1 (e8b89.. x2 x3 x4 x5)) ⟶ x1 x0
Theorem 81997.. : ∀ 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 ⟶ 0a1fb.. (e8b89.. x0 x1 x2 x3) (proof)
Theorem b2f98.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 . 0a1fb.. (e8b89.. x0 x1 x2 x3) ⟶ ∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x4 x5) x0 (proof)
Theorem e8b51.. : ∀ x0 . ∀ x1 : (ι → ο) → ο . ∀ x2 : ι → ι → ι . ∀ x3 . 0a1fb.. (e8b89.. x0 x1 x2 x3) ⟶ prim1 x3 x0 (proof)
Theorem 4e54b.. : ∀ x0 . 0a1fb.. x0 ⟶ x0 = e8b89.. (f482f.. x0 4a7ef..) (decode_c (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Definition ac2cd.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (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..))))
Theorem 720ab.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι → ι . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ ac2cd.. (e8b89.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)
Definition 43515.. := λ x0 . λ x1 : ι → ((ι → ο) → ο) → (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..))))
Theorem 16888.. : ∀ x0 : ι → ((ι → ο) → ο) → (ι → ι → ι) → ι → ο . ∀ x1 . ∀ x2 : (ι → ο) → ο . ∀ x3 : ι → ι → ι . ∀ x4 . (∀ x5 : (ι → ο) → ο . (∀ x6 : ι → ο . (∀ x7 . x6 x7 ⟶ prim1 x7 x1) ⟶ iff (x2 x6) (x5 x6)) ⟶ ∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x3 x7 x8 = x6 x7 x8) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4) ⟶ 43515.. (e8b89.. x1 x2 x3 x4) x0 = x0 x1 x2 x3 x4 (proof)