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Proofgold Signed Transaction

vin
PrEvg../ddd59..
PUYKa../892b3..
vout
PrEvg../1344f.. 0.23 bars
TMGH5../1ad48.. ownership of f5f40.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGyb../443f5.. ownership of 0d5db.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUd6../56002.. ownership of 0d265.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGJY../56cc9.. ownership of f3a72.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdup../e010e.. ownership of b5a61.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKvi../ac260.. ownership of 3109f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKTk../46f56.. ownership of 666f7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHTX../770d6.. ownership of 302ac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLrX../4d37b.. ownership of 184a5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZJr../5ee16.. ownership of 59617.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM2R../7fb14.. ownership of 628aa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJcX../26824.. ownership of b5cb2.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMccN../5a981.. ownership of 59175.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZUz../3dbf7.. ownership of c4b4b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPtH../1a564.. ownership of 6042c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRNN../b6b33.. ownership of f8827.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNif../1f77f.. ownership of a05e5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUpH../474b2.. ownership of 25536.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWpC../92ffb.. ownership of f5703.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPMt../8d636.. ownership of a2784.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMS9s../42afa.. ownership of 599c1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbN2../83ba4.. ownership of 99015.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLhh../c7fdd.. ownership of e8f5c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdZm../2ad1c.. ownership of ddb82.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQBy../779c6.. ownership of 31d04.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWyJ../6a11c.. ownership of d8226.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFUj../81cc5.. ownership of cee04.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQX4../264d1.. ownership of 303a5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXGA../59d20.. ownership of 337f1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc37../3428d.. ownership of 95303.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPiW../757f3.. ownership of 71db9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPq3../c94ba.. ownership of 1577e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW11../67094.. ownership of 66838.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaWi../95a35.. ownership of e1da6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVzN../953fd.. ownership of 5bcbc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEj2../6e34a.. ownership of 4d3b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSgo../24954.. ownership of 7ad4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdvo../f1d0b.. ownership of 8815c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMgH../33119.. ownership of 0ad60.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJW5../f1af9.. ownership of dce4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdW5../a6108.. ownership of 75db4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ1H../78b52.. ownership of b65d3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV9q../c1983.. ownership of c26d3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFTN../4e853.. ownership of 41c72.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPbR../971e2.. ownership of fbb67.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaXt../a335f.. ownership of 178b6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXtK../983fb.. ownership of 32345.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT79../bedc5.. ownership of 983b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML3B../97444.. ownership of 81cf9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGWx../1fc97.. ownership of 71bff.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPP6../9f35d.. ownership of bf16f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYCL../f507c.. ownership of c147e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLKJ../d9be1.. ownership of b2875.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcKq../7441e.. ownership of 2ee82.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJnw../d94bd.. ownership of 6231a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ5d../8c55f.. ownership of cbf73.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX6F../02adc.. ownership of 0ba00.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWMu../81e51.. ownership of 717b4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN5y../4dbce.. ownership of c3940.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN5w../8f76e.. ownership of cfa40.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKWH../dcb9f.. ownership of 8838b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR3e../74a77.. ownership of 2dacc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb17../31da4.. ownership of 2be22.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPnt../f8abd.. ownership of 90321.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP5a../d35b4.. ownership of c6f4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRwP../03b3e.. ownership of f89c6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXoH../1316d.. ownership of d680e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUwq../c9ff3.. ownership of 68a0f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZwd../e6548.. ownership of cfe45.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVjX../87b4c.. ownership of ec91d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaLd../86679.. ownership of 4a032.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZqB../de670.. ownership of ad900.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTVD../f9bc6.. ownership of 26988.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaZn../1caff.. ownership of 7c05d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNEt../69b51.. ownership of a1578.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSyW../643d0.. ownership of bfa93.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZLU../7d2b9.. ownership of ec03d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN3C../70979.. ownership of 1b5c8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZaF../ea6df.. ownership of 021d5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSdP../f191b.. ownership of 74331.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTE6../b328f.. ownership of 76e7a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQq2../9e389.. ownership of dd50a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNez../43e21.. ownership of d4d99.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVtQ../cc4a1.. ownership of 9ec78.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWv6../42cdb.. ownership of b2c86.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMWs../9236a.. ownership of 41eae.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSk7../e3691.. ownership of 802db.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcPE../865d2.. ownership of b80ef.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML68../3b724.. ownership of 6a558.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb3D../f04aa.. ownership of e00ac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbgG../6be4b.. ownership of aceec.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd3g../4c459.. ownership of bfe95.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKHa../cc6b8.. ownership of 286c8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQZM../542f3.. ownership of 65d72.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQRX../901e6.. ownership of 2694e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMDm../37067.. ownership of 24593.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPSD../5109f.. ownership of 38186.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJvF../7103f.. ownership of 41657.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU44../548b6.. ownership of 3e1fd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWaB../4f66c.. ownership of cc99f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU5i../5ab54.. ownership of 5bb2c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF4M../ff90f.. ownership of 919da.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVkX../d5b4b.. ownership of 4052b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb2L../d3314.. ownership of 57856.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcxu../0379b.. ownership of 76fc8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMti../dff91.. ownership of ecdf1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTFx../943bc.. ownership of ce1e0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSCV../6e64e.. ownership of ec17a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcB4../5cf8f.. ownership of 5af5a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF3G../bc359.. ownership of 89df6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNDJ../4ed2b.. ownership of 322b6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZrh../049b3.. ownership of bee74.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP5d../cc737.. ownership of 961c9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKa4../9e8b6.. ownership of d3913.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKJ5../116a9.. ownership of 39510.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV8Q../9505b.. ownership of 51d19.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSXx../b2ab3.. ownership of f93ce.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYGY../d53a1.. ownership of 8a0b9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKnq../6b0b8.. ownership of 8024e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYrZ../1366c.. ownership of 67796.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSxA../13d9a.. ownership of 778d0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRaR../6ff58.. ownership of 85e99.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMchg../dde92.. ownership of cae44.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbXR../f7cba.. ownership of e4241.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPsh../ea941.. ownership of 3fc70.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJUv../5b0e4.. ownership of 7d246.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQHW../ade74.. ownership of 8ebac.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSgv../64d77.. ownership of 042fb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ2P../f7437.. ownership of 27ce6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLrC../3834d.. ownership of c1003.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdJf../42f42.. ownership of 45260.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNue../ac41f.. ownership of 35854.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMK4e../16169.. ownership of fcc08.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb5K../ee226.. ownership of a5be1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYi3../bd373.. ownership of 021fc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQkU../caa6b.. ownership of cb2da.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPoU../42edd.. ownership of 0db25.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdAd../629ea.. ownership of c64bc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMU6G../e0849.. ownership of 5f754.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQX1../efe01.. ownership of 1a243.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFQQ../e6edd.. ownership of d1a4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSDe../a06f2.. ownership of a0d93.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLDs../7ed04.. ownership of 0841f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTYh../e27b7.. ownership of e6dfc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXwi../389a1.. ownership of a2722.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMsB../35ff0.. ownership of 06630.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHXY../62544.. ownership of 9e738.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSuq../e8c12.. ownership of be86c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKqW../3c803.. ownership of c758a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFgf../e6012.. ownership of 6eb26.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW9C../ab686.. ownership of be935.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGVv../841fc.. ownership of df8e4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNp9../d7b26.. ownership of 8160a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQAs../96d41.. ownership of 2260f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRx9../8857c.. ownership of 50941.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXzk../85def.. ownership of 4d3e9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMan8../56ce8.. ownership of 8099c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHzE../78e52.. ownership of 62c81.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMku../bc64b.. ownership of 18c93.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZDA../e409f.. ownership of f79fc.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYdJ../9e513.. ownership of 94799.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaF5../4002e.. ownership of ee6e0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGpU../3ed22.. ownership of 02b3f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJHb../84787.. ownership of 2d72f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbF4../11449.. ownership of bbb56.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTRs../21d0e.. ownership of d88f4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdNm../cd27b.. ownership of d74ee.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYT8../fddcd.. ownership of 7b976.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNVm../8b282.. ownership of c53cd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHcj../78501.. ownership of 17885.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFer../da1f2.. ownership of 217fd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKjs../2a984.. ownership of 4eca0.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMas8../20c1f.. ownership of bb05a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSU9../479fb.. ownership of d5e21.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT3t../304ea.. ownership of 81528.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMa9R../6b997.. ownership of 36257.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSvf../e7ee1.. ownership of f1fbf.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNqV../39e4a.. ownership of fa19e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQEU../3dd33.. ownership of 9b6e8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRYw../f6e9a.. ownership of 65e60.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUfK2../54bbc.. 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
Definition 9b6e8.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : 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..)) (0fc90.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 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 9e738.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9b6e8.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem a2722.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . x0 = f482f.. (9b6e8.. 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 0841f.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9b6e8.. 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 d1a4a.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (9b6e8.. 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
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Theorem 5f754.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9b6e8.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x3 x6 = f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 (proof)
Theorem 0db25.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ x2 x5 = f482f.. (f482f.. (9b6e8.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 (proof)
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
Theorem 021fc.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9b6e8.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem fcc08.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . x3 = f482f.. (9b6e8.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (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 45260.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι . ∀ x4 x5 . x0 = 9b6e8.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 27ce6.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . x4 = f482f.. (9b6e8.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (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 8ebac.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι . ∀ x6 x7 x8 x9 . 9b6e8.. x0 x2 x4 x6 x8 = 9b6e8.. 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)) (x6 = x7)) (x8 = x9) (proof)
Known 4402a.. : ∀ x0 . ∀ x1 x2 : ι → ι . (∀ x3 . prim1 x3 x0 ⟶ x1 x3 = x2 x3) ⟶ 0fc90.. x0 x1 = 0fc90.. x0 x2
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 3fc70.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι . ∀ x5 x6 . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ x3 x7 = x4 x7) ⟶ 9b6e8.. x0 x1 x3 x5 x6 = 9b6e8.. x0 x2 x4 x5 x6 (proof)
Definition f1fbf.. := 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 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (9b6e8.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem cae44.. : ∀ 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 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ f1fbf.. (9b6e8.. x0 x1 x2 x3 x4) (proof)
Theorem 778d0.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . f1fbf.. (9b6e8.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 8024e.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . f1fbf.. (9b6e8.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ prim1 (x2 x5) x0 (proof)
Theorem f93ce.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . f1fbf.. (9b6e8.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 39510.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι . ∀ x3 x4 . f1fbf.. (9b6e8.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem 961c9.. : ∀ x0 . f1fbf.. x0 ⟶ x0 = 9b6e8.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 81528.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 322b6.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : 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 . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ 81528.. (9b6e8.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition bb05a.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (f482f.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 5af5a.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι) → ι → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : 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 . (∀ x8 . prim1 x8 x1 ⟶ x3 x8 = x7 x8) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ bb05a.. (9b6e8.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Param d2155.. : ι → (ι → ι → ο) → ι
Param 1216a.. : ι → (ι → ο) → ι
Definition 217fd.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι → ο . 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..)) (d2155.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) (1216a.. x0 x4)))))
Theorem ce1e0.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = 217fd.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 76fc8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . x0 = f482f.. (217fd.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 4052b.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = 217fd.. 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 5bb2c.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (217fd.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (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 3e1fd.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = 217fd.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 38186.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = 2b2e3.. (f482f.. (217fd.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (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 2694e.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = 217fd.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem 286c8.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (217fd.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem aceec.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 : ι → ο . x0 = 217fd.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x5 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x6 (proof)
Theorem 6a558.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . ∀ x5 . prim1 x5 x0 ⟶ x4 x5 = decode_p (f482f.. (217fd.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (proof)
Theorem 802db.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 x8 x9 : ι → ο . 217fd.. x0 x2 x4 x6 x8 = 217fd.. 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 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 b2c86.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ 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 ⟶ iff (x3 x9 x10) (x4 x9 x10)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x5 x9) (x6 x9)) ⟶ (∀ x9 . prim1 x9 x0 ⟶ iff (x7 x9) (x8 x9)) ⟶ 217fd.. x0 x1 x3 x5 x7 = 217fd.. x0 x2 x4 x6 x8 (proof)
Definition c53cd.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι → ο . ∀ x5 x6 : ι → ο . x1 (217fd.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem d4d99.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . c53cd.. (217fd.. x0 x1 x2 x3 x4) (proof)
Theorem 76e7a.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 : ι → ο . c53cd.. (217fd.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Known iff_refl : ∀ x0 : ο . iff x0 x0
Theorem 021d5.. : ∀ x0 . c53cd.. x0 ⟶ x0 = 217fd.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (proof)
Definition d74ee.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem ec03d.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ 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 → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (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) ⟶ d74ee.. (217fd.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition bbb56.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))
Theorem a1578.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ 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 → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (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) ⟶ bbb56.. (217fd.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 02b3f.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι → ο . 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..)) (d2155.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (1216a.. x0 x3) x4))))
Theorem 26988.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = 02b3f.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 4a032.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . x0 = f482f.. (02b3f.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem cfe45.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = 02b3f.. 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 d680e.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (02b3f.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem c6f4a.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = 02b3f.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem 2be22.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = 2b2e3.. (f482f.. (02b3f.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 8838b.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = 02b3f.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ x4 x6 = decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (proof)
Theorem c3940.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 x5 . prim1 x5 x0 ⟶ x3 x5 = decode_p (f482f.. (02b3f.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x5 (proof)
Theorem 0ba00.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 : ι → ο . ∀ x5 . x0 = 02b3f.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem 6231a.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . x4 = f482f.. (02b3f.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem b2875.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 : ι → ο . ∀ x8 x9 . 02b3f.. x0 x2 x4 x6 x8 = 02b3f.. 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 bf16f.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ 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 ⟶ iff (x3 x8 x9) (x4 x8 x9)) ⟶ (∀ x8 . prim1 x8 x0 ⟶ iff (x5 x8) (x6 x8)) ⟶ 02b3f.. x0 x1 x3 x5 x7 = 02b3f.. x0 x2 x4 x6 x7 (proof)
Definition 94799.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι → ο . ∀ x5 : ι → ο . ∀ x6 . prim1 x6 x2 ⟶ x1 (02b3f.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 81cf9.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . prim1 x4 x0 ⟶ 94799.. (02b3f.. x0 x1 x2 x3 x4) (proof)
Theorem 32345.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . 94799.. (02b3f.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem fbb67.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 : ι → ο . ∀ x4 . 94799.. (02b3f.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem c26d3.. : ∀ x0 . 94799.. x0 ⟶ x0 = 02b3f.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition 18c93.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 75db4.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ 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 → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (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) ⟶ 18c93.. (02b3f.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 8099c.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 0ad60.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ 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 → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (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) ⟶ 8099c.. (02b3f.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition 50941.. := λ x0 . λ x1 : ι → ι → ι . λ x2 : ι → ι → ο . 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..)) (d2155.. x0 x2) (If_i (x5 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 x4))))
Theorem 7ad4a.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = 50941.. x1 x2 x3 x4 x5 ⟶ x1 = f482f.. x0 4a7ef.. (proof)
Theorem 5bcbc.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . x0 = f482f.. (50941.. x0 x1 x2 x3 x4) 4a7ef.. (proof)
Theorem 66838.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = 50941.. 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 71db9.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x1 x5 x6 = e3162.. (f482f.. (50941.. x0 x1 x2 x3 x4) (4ae4a.. 4a7ef..)) x5 x6 (proof)
Theorem 337f1.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = 50941.. x1 x2 x3 x4 x5 ⟶ ∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ x3 x6 x7 = 2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..))) x6 x7 (proof)
Theorem cee04.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ x2 x5 x6 = 2b2e3.. (f482f.. (50941.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) x5 x6 (proof)
Theorem 31d04.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = 50941.. x1 x2 x3 x4 x5 ⟶ x4 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem e8f5c.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . x3 = f482f.. (50941.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (proof)
Theorem 599c1.. : ∀ x0 x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . x0 = 50941.. x1 x2 x3 x4 x5 ⟶ x5 = f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem f5703.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . x4 = f482f.. (50941.. x0 x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (proof)
Theorem a05e5.. : ∀ x0 x1 . ∀ x2 x3 : ι → ι → ι . ∀ x4 x5 : ι → ι → ο . ∀ x6 x7 x8 x9 . 50941.. x0 x2 x4 x6 x8 = 50941.. 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 6042c.. : ∀ x0 . ∀ x1 x2 : ι → ι → ι . ∀ x3 x4 : ι → ι → ο . ∀ x5 x6 . (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x1 x7 x8 = x2 x7 x8) ⟶ (∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ iff (x3 x7 x8) (x4 x7 x8)) ⟶ 50941.. x0 x1 x3 x5 x6 = 50941.. x0 x2 x4 x5 x6 (proof)
Definition 8160a.. := λ x0 . ∀ x1 : ι → ο . (∀ x2 . ∀ x3 : ι → ι → ι . (∀ x4 . prim1 x4 x2 ⟶ ∀ x5 . prim1 x5 x2 ⟶ prim1 (x3 x4 x5) x2) ⟶ ∀ x4 : ι → ι → ο . ∀ x5 . prim1 x5 x2 ⟶ ∀ x6 . prim1 x6 x2 ⟶ x1 (50941.. x2 x3 x4 x5 x6)) ⟶ x1 x0
Theorem 59175.. : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . prim1 x2 x0 ⟶ ∀ x3 . prim1 x3 x0 ⟶ prim1 (x1 x2 x3) x0) ⟶ ∀ x2 : ι → ι → ο . ∀ x3 . prim1 x3 x0 ⟶ ∀ x4 . prim1 x4 x0 ⟶ 8160a.. (50941.. x0 x1 x2 x3 x4) (proof)
Theorem 628aa.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . 8160a.. (50941.. x0 x1 x2 x3 x4) ⟶ ∀ x5 . prim1 x5 x0 ⟶ ∀ x6 . prim1 x6 x0 ⟶ prim1 (x1 x5 x6) x0 (proof)
Theorem 184a5.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . 8160a.. (50941.. x0 x1 x2 x3 x4) ⟶ prim1 x3 x0 (proof)
Theorem 666f7.. : ∀ x0 . ∀ x1 : ι → ι → ι . ∀ x2 : ι → ι → ο . ∀ x3 x4 . 8160a.. (50941.. x0 x1 x2 x3 x4) ⟶ prim1 x4 x0 (proof)
Theorem b5a61.. : ∀ x0 . 8160a.. x0 ⟶ x0 = 50941.. (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (proof)
Definition be935.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ι → ι . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem 0d265.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ι → ι . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ be935.. (50941.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)
Definition c758a.. := λ x0 . λ x1 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ι → ο . x1 (f482f.. x0 4a7ef..) (e3162.. (f482f.. x0 (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. x0 (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. x0 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))
Theorem f5f40.. : ∀ x0 : ι → (ι → ι → ι) → (ι → ι → ο) → ι → ι → ο . ∀ x1 . ∀ x2 : ι → ι → ι . ∀ x3 : ι → ι → ο . ∀ x4 x5 . (∀ x6 : ι → ι → ι . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ x2 x7 x8 = x6 x7 x8) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5) ⟶ c758a.. (50941.. x1 x2 x3 x4 x5) x0 = x0 x1 x2 x3 x4 x5 (proof)