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Proofgold Signed Transaction

vin
PrKAk../c2d61..
PUMrS../3d282..
vout
PrKAk../f3a46.. 24.98 bars
TMcVe../5d1f7.. ownership of 422f0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKZY../2d24a.. ownership of 3ad8f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa3G../eed46.. ownership of ddc02.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH69../a0da2.. ownership of 1cac9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZp7../c4948.. ownership of d468d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKNq../4521b.. ownership of fce37.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYD1../2ecb3.. ownership of 3f145.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPys../3ff49.. ownership of 9828a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYCv../04ab5.. ownership of 73173.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGXM../a708c.. ownership of fa26d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFPE../33727.. ownership of 1bc9e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGaG../9b9b4.. ownership of dcceb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQde../25117.. ownership of 1e035.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPzb../365b0.. ownership of c168e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM7d../f4b59.. ownership of b94ff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZLM../54628.. ownership of cdd5b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdW2../c479c.. ownership of a809c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHi6../8ab48.. ownership of 7580d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMbX../43cdb.. ownership of e8d05.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ83../6aa68.. ownership of 33f97.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSq8../df8b8.. ownership of 5d78f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGVw../bdbdb.. ownership of 39de3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTMf../a250d.. ownership of c4598.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSK1../4a20b.. ownership of e01c1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTsJ../799f4.. ownership of 4d4e3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJGw../f60f9.. ownership of 1f8c9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZay../efe98.. ownership of 89e9d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcTb../7200c.. ownership of eefcb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG12../44b89.. ownership of e5b54.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWKC../10f0b.. ownership of e5e5f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTQg../91c2c.. ownership of 7b79f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQTn../454ce.. ownership of 47b32.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJcV../113b8.. ownership of d2b30.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXJT../6b793.. ownership of d577c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQQJ../8aa0d.. ownership of 7c19d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbHA../ecffd.. ownership of 87e66.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXpP../f7c4c.. ownership of 24f4f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHHE../c94bf.. ownership of bd805.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGPd../5d0a8.. ownership of 242ff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT3A../4e607.. ownership of d274a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT8u../6a1e2.. ownership of a296b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMS2B../24caf.. ownership of 897e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd3n../94f2b.. ownership of 619d5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWee../72c2e.. ownership of aec46.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVFq../03b7b.. ownership of f7980.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcwp../bcc77.. ownership of 0062b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMHM../33090.. ownership of 2ca4b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPhH../f1c4b.. ownership of eda77.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQiX../73f17.. ownership of 38e2b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZeV../953d1.. ownership of 826de.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHSY../7a491.. ownership of 9b39d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHHg../9ee7b.. ownership of 412a0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaoD../843e1.. ownership of 836a9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJPC../b1eb0.. ownership of a43ed.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc7P../9c9d6.. ownership of d0777.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWEc../68540.. ownership of 58d49.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNCa../a783d.. ownership of e32d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa4n../a3f0c.. ownership of d017d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZYL../bcdf5.. ownership of 85b9b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMkq../e7b5b.. ownership of bbfd6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQnx../fd338.. ownership of 73020.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJWk../53e62.. ownership of 57ed9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQtN../fdd60.. ownership of 8307f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcgB../be687.. ownership of a0111.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYxB../b6762.. ownership of 74356.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWNe../5aff1.. ownership of f8fac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFke../15b14.. ownership of 45d05.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMPL../dd91e.. ownership of 6672e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRg8../42f74.. ownership of bdaba.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK9i../a26c3.. ownership of 060a2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFm3../2b100.. ownership of 1b277.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWhx../7185f.. ownership of 62453.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSm9../613e7.. ownership of cb757.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUcQ../537dc.. ownership of 6f396.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHTe../75327.. ownership of 90132.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRQc../81da3.. ownership of a704b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQFp../cb0ce.. ownership of 78584.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH44../c0221.. ownership of 4caf2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM2g../708a8.. ownership of 2148c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHuf../a1d65.. ownership of 07844.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcEF../06bb0.. ownership of 1a9ad.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRjv../eadcd.. ownership of 29828.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNBs../81a11.. ownership of c34a4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNuG../effea.. ownership of 478b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa8w../a42d7.. ownership of a6b66.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb3i../e0580.. ownership of 9db04.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdXW../15b11.. ownership of 8699c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR2H../82ef3.. ownership of e61b9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYh9../5ac3c.. ownership of 50df3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaEz../4c558.. ownership of 2d505.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVe7../3316a.. ownership of f7e1f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb34../9299a.. ownership of ef075.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ6M../d335a.. ownership of fae3b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd68../0717d.. ownership of 77371.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK1j../1dfc6.. ownership of 4ba72.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcqM../0fc1f.. ownership of e1654.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXwj../95227.. ownership of ffd6d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSjm../ed59b.. ownership of 003fe.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGnB../f22e0.. ownership of addbb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXyP../b9ea7.. ownership of 6bfde.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRxr../af4d4.. ownership of f8edd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMam7../68175.. ownership of 946d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJfG../ea3c3.. ownership of d0dc0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP93../c7a8e.. ownership of c207b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TManF../0c26c.. ownership of 993d3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYH4../7739a.. ownership of dca0b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGvC../4983a.. ownership of e6bc5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXcj../385b5.. ownership of 056d2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ4h../4f595.. ownership of e3b7c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQqv../87784.. ownership of f0bca.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcQk../c30c7.. ownership of bce93.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEk5../5f27a.. ownership of 8ebec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNak../1dfd7.. ownership of bbc04.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNJV../4b3bc.. ownership of 3c18b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZbt../4fc8a.. ownership of e68e5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXg6../dd4c4.. ownership of 2e1e6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ9p../fdb20.. ownership of 38d44.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUt1../46833.. ownership of 587e0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF5t../757f9.. ownership of fa488.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMby5../33d10.. ownership of e97fb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSEq../0d1ad.. ownership of 451b8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcv2../da34a.. ownership of 04c93.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLxT../b4334.. ownership of ac2a2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ6M../5c1ab.. ownership of 31888.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUwN../e873a.. ownership of 65946.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGKd../4c3ca.. ownership of ed827.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRNq../4c720.. ownership of a27e7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMrQ../66d64.. ownership of ba3ab.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGLL../cedaa.. ownership of 1c75e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLJr../bf3f1.. ownership of ee374.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEp7../3845e.. ownership of 90e82.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP5g../e7b35.. ownership of 36983.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWby../190ce.. ownership of 797e1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZRV../bf742.. ownership of 74da7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPRS../f4d8d.. ownership of 4e2bc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLyZ../76800.. ownership of e2341.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQxk../8aace.. ownership of 1ed3c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYk2../fb57b.. ownership of 2a396.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUae../a7464.. ownership of bc41a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQgV../d88a6.. ownership of e2a88.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJFJ../d73a5.. ownership of 33c92.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYXm../6de53.. ownership of ef16a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHwo../777c4.. ownership of 99c13.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPxu../23088.. ownership of c2ca3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbAx../61031.. ownership of afa00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcTE../e2e81.. ownership of 23d86.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU5u../f4e37.. ownership of 4e3d3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbGw../25cb6.. ownership of c341b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNrr../61a57.. ownership of f88de.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWFY../01e24.. ownership of 101f6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJa9../ea00c.. ownership of 4e608.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMr8../defbe.. ownership of e5112.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLnp../8fb2f.. ownership of af09b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZmE../22d74.. ownership of 5c618.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGRo../e69a8.. ownership of 76ccd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFFQ../093f2.. ownership of b8ca9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKeD../40d6d.. ownership of d0dcf.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVbr../29d4a.. ownership of ccac1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMrA../089a4.. ownership of c3510.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQfc../64541.. ownership of 30b12.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHnk../083c4.. ownership of 92512.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWNg../e3e81.. ownership of d2e16.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSYS../62473.. ownership of 3f0d0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPk3../322ee.. ownership of be86d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb4X../b935e.. ownership of c77b5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYSA../ca861.. ownership of ff1e8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGoU../4c471.. ownership of 32202.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYiB../bee31.. ownership of b9c61.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLhH../08872.. ownership of c3c22.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVHr../75f0f.. ownership of 35ad2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYrn../008ae.. ownership of 160e6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQTq../e9b65.. ownership of 373d4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML3i../edb61.. ownership of 1e782.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRGX../57997.. ownership of b69ba.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdh1../a8cec.. ownership of 866d7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLRm../e534d.. ownership of fbc56.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJDY../691e7.. ownership of 9bdf0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTiv../169f5.. ownership of 0c005.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbte../40d57.. ownership of 33bf8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM57../1ebfc.. ownership of 92322.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa1g../9dce0.. ownership of f7962.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZCc../1dd31.. ownership of dca8f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUhXL../e8961.. doc published by PrGxv..
Param 0fc90.. : ι → (ι → ι) → ι
Param 4ae4a.. : ι → ι
Param 4a7ef.. : ι
Param If_i : ο → ι → ι → ι
Param eb53d.. : ι → CT2 ι
Param 1216a.. : ι → (ι → ο) → ι
Definition f7962.. := λ x0 . λ x1 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..) (eb53d.. 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 f88de.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = f7962.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 4e3d3.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . x0 = f482f.. (f7962.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Param e3162.. : ι → ι → ι → ι
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 35054.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ e3162.. (eb53d.. x0 x1) x2 x3 = x1 x2 x3
Theorem afa00.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = f7962.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 x7 (proof)
Theorem 99c13.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (f7962.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (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
Theorem 33c92.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = f7962.. 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 bc41a.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (f7962.. 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 1ed3c.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = f7962.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 4e2bc.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (f7962.. 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 797e1.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . x0 = f7962.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 90e82.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (f7962.. 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 1c75e.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι → ι . ∀ x6 x7 x8 x9 : ι → ο . f7962.. x0 x2 x4 x6 x8 = f7962.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11)) (∀ 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
Theorem a27e7.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι → ι . ∀ x5 x6 x7 x8 : ι → ο . (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x1 x9 x10 = x2 x9 x10) ⟶ (∀ 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)) ⟶ f7962.. x0 x1 x3 x5 x7 = f7962.. x0 x2 x4 x6 x8 (proof)
Definition 33bf8.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 x6 : ι → ο . x1 (f7962.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 65946.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 x4 : ι → ο . 33bf8.. (f7962.. x0 x1 x2 x3 x4) (proof)
Theorem ac2a2.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . 33bf8.. (f7962.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 451b8.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ο . 33bf8.. (f7962.. 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 fa488.. : ∀ x0 . 33bf8.. x0 ⟶ x0 = f7962.. (f482f.. x0 4a7ef..) (e3162.. (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 9bdf0.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (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 38d44.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 9bdf0.. (f7962.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 866d7.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (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 e68e5.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 866d7.. (f7962.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 1e782.. := λ x0 . λ x1 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..) (eb53d.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) x4))))
Theorem bbc04.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 1e782.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem bce93.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x0 = f482f.. (1e782.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem e3b7c.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 1e782.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 x7 (proof)
Theorem e6bc5.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (1e782.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 993d3.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 1e782.. 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 d0dc0.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (1e782.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem f8edd.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 1e782.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem addbb.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (1e782.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem ffd6d.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . x0 = 1e782.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 4ba72.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . x4 = f482f.. (1e782.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem fae3b.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι → ι . ∀ x6 x7 : ι → ο . ∀ x8 x9 . 1e782.. x0 x2 x4 x6 x8 = 1e782.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11)) (∀ 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 f7e1f.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι → ι . ∀ x5 x6 : ι → ο . ∀ x7 . (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x1 x8 x9 = x2 x8 x9) ⟶ (∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x3 x8 x9 = x4 x8 x9) ⟶ (∀ x8 . prim1 x8 x0 ⟶ iff (x5 x8) (x6 x8)) ⟶ 1e782.. x0 x1 x3 x5 x7 = 1e782.. x0 x2 x4 x6 x7 (proof)
Definition 160e6.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 : ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (1e782.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 50df3.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ 160e6.. (1e782.. x0 x1 x2 x3 x4) (proof)
Theorem 8699c.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . 160e6.. (1e782.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem a6b66.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . 160e6.. (1e782.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem c34a4.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 : ι → ο . ∀ x4 . 160e6.. (1e782.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 1a9ad.. : ∀ x0 . 160e6.. x0 ⟶ x0 = 1e782.. (f482f.. x0 4a7ef..) (e3162.. (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 c3c22.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (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 2148c.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ι → ι . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ c3c22.. (1e782.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 32202.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (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 78584.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → (ι → ο) → ι → ο . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 : ι → ο . ∀ x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 32202.. (1e782.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition c77b5.. := λ x0 . λ x1 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..) (eb53d.. x0 x1) (If_i (x5 = 4ae4a.. (4ae4a.. 4a7ef..)) (eb53d.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))
Theorem 90132.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . x0 = c77b5.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem cb757.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . x0 = f482f.. (c77b5.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 1b277.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . x0 = c77b5.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 x7 (proof)
Theorem bdaba.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (c77b5.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 45d05.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . x0 = c77b5.. 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 74356.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = e3162.. (f482f.. (c77b5.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 8307f.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . x0 = c77b5.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 73020.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . x3 = f482f.. (c77b5.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 85b9b.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . x0 = c77b5.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem e32d8.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . x4 = f482f.. (c77b5.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem d0777.. : ∀ x0 x1 . ∀ x2 x3 x4 x5 : ι → ι → ι . ∀ x6 x7 x8 x9 . c77b5.. x0 x2 x4 x6 x8 = c77b5.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11)) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x4 x10 x11 = x5 x10 x11)) (x6 = x7)) (x8 = x9) (proof)
Theorem 836a9.. : ∀ x0 . ∀ x1 x2 x3 x4 : ι → ι → ι . ∀ x5 x6 . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x3 x7 x8 = x4 x7 x8) ⟶ c77b5.. x0 x1 x3 x5 x6 = c77b5.. x0 x2 x4 x5 x6 (proof)
Definition 3f0d0.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι → ι . (∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ prim1 (x4 x5 x6) x2) ⟶ ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (c77b5.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 9b39d.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ι . (∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ prim1 (x2 x3 x4) x0) ⟶ ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 3f0d0.. (c77b5.. x0 x1 x2 x3 x4) (proof)
Theorem 38e2b.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . 3f0d0.. (c77b5.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 2ca4b.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . 3f0d0.. (c77b5.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x2 x5 x6) x0 (proof)
Theorem f7980.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . 3f0d0.. (c77b5.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 619d5.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 . 3f0d0.. (c77b5.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem a296b.. : ∀ x0 . 3f0d0.. x0 ⟶ x0 = c77b5.. (f482f.. x0 4a7ef..) (e3162.. (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 92512.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 242ff.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 92512.. (c77b5.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition c3510.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (e3162.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 24f4f.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ι) → ι → ι → ο . ∀ x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ c3510.. (c77b5.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Definition d0dcf.. := λ x0 . λ x1 : ι → ι → ι . 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..) (eb53d.. 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 7c19d.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = d0dcf.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem d2b30.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 x5 : ι → ι → ο . x5 x0 (f482f.. (d0dcf.. x0 x1 x2 x3 x4) 4a7ef..) ⟶ x5 (f482f.. (d0dcf.. x0 x1 x2 x3 x4) 4a7ef..) x0 (proof)
Theorem 7b79f.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = d0dcf.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x2 x6 x7 = e3162.. (f482f.. x0 (4ae4a.. 4a7ef..)) x6 x7 (proof)
Theorem e5b54.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (d0dcf.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 89e9d.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = d0dcf.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 4d4e3.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (d0dcf.. 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 c4598.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = d0dcf.. 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 5d78f.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x3 x5 x6 = 2b2e3.. (f482f.. (d0dcf.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 x6 (proof)
Theorem e8d05.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . x0 = d0dcf.. 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 a809c.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x4 x5 x6 = 2b2e3.. (f482f.. (d0dcf.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 x6 (proof)
Theorem b94ff.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι . ∀ x6 x7 x8 x9 : ι → ι → ο . d0dcf.. x0 x2 x4 x6 x8 = d0dcf.. x1 x3 x5 x7 x9 ⟶ and (and (and (and (x0 = x1) (∀ x10 . prim1 x10 x0 ⟶ ∀ x11 . prim1 x11 x0 ⟶ x2 x10 x11 = x3 x10 x11)) (∀ 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 1e035.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι . ∀ x5 x6 x7 x8 : ι → ι → ο . (∀ x9 . prim1 x9 x0 ⟶ ∀ x10 . prim1 x10 x0 ⟶ x1 x9 x10 = x2 x9 x10) ⟶ (∀ 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)) ⟶ d0dcf.. x0 x1 x3 x5 x7 = d0dcf.. x0 x2 x4 x6 x8 (proof)
Definition 76ccd.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι . (∀ x5 . prim1 x5 x2 ⟶ prim1 (x4 x5) x2) ⟶ ∀ x5 x6 : ι → ι → ο . x1 (d0dcf.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 1bc9e.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ prim1 (x2 x3) x0) ⟶ ∀ x3 x4 : ι → ι → ο . 76ccd.. (d0dcf.. x0 x1 x2 x3 x4) (proof)
Theorem 73173.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . 76ccd.. (d0dcf.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 3f145.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 : ι → ι → ο . 76ccd.. (d0dcf.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem d468d.. : ∀ x0 . 76ccd.. x0 ⟶ x0 = d0dcf.. (f482f.. x0 4a7ef..) (e3162.. (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 af09b.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (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 ddc02.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ af09b.. (d0dcf.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 4e608.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (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 422f0.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → (ι → ι → ο) → (ι → ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 : ι → ι → ο . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ 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) ⟶ 4e608.. (d0dcf.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)