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Proofgold Signed Transaction

vin
Pr7wB../02da0..
PUNFY../5cc77..
vout
Pr7wB../20304.. 0.07 bars
TMQV7../f13c2.. ownership of f5522.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRpJ../6b2d4.. ownership of 7593a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMES../46b4f.. ownership of 3b41c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYaf../4f3b4.. ownership of 36f23.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc9o../00b6f.. ownership of 5ce4d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWt3../54781.. ownership of 9273f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTFj../29d39.. ownership of c88a1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJYU../ab3fa.. ownership of a126c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPax../11df2.. ownership of 9a6d8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZEo../cb484.. ownership of 56a9c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYSf../bc6dd.. ownership of a62b0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdLr../57d59.. ownership of 955eb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYrW../14be7.. ownership of 759ba.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUWL../d298e.. ownership of 1bb33.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRGg../c69b7.. ownership of cce05.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVuN../02516.. ownership of 8b528.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKap../5937b.. ownership of 3887e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGnP../6b64a.. ownership of 650a0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSEG../5e183.. ownership of c7b0c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbBv../861bb.. ownership of 2a256.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVFC../972a7.. ownership of ce596.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQFv../86088.. ownership of 53706.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMH8E../0ef8d.. ownership of 68e20.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGvp../77056.. ownership of fd4eb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFp1../d51bc.. ownership of 0040c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLMv../b071b.. ownership of 4c315.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHjf../60050.. ownership of 43e16.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML4G../a0c7c.. ownership of 93c51.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXBe../66305.. ownership of da995.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaET../f4291.. ownership of 38ba6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTo9../66009.. ownership of a7d47.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNKM../29f62.. ownership of 898bd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdpw../7b7a4.. ownership of ef4b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXXh../6b958.. ownership of bd42f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWyF../dadab.. ownership of 77ec5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG8A../b1995.. ownership of 8b242.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHeQ../3a694.. ownership of 6cbca.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdnq../89fd3.. ownership of 9968e.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMR95../90924.. ownership of e5f60.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWAn../67063.. ownership of 82bda.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGK1../902d3.. ownership of c28c7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML1q../24e76.. ownership of 13559.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMZw../3f685.. ownership of 9e014.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPE8../87bab.. ownership of e6f99.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFKC../6917d.. ownership of 6274f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUKf../8ff9f.. ownership of 3e627.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLSP../36bba.. ownership of b8971.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNpo../f20cf.. ownership of db2ed.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVzP../ea58e.. ownership of 52fd9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLVP../74d95.. ownership of 8585a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKnW../0ba08.. ownership of 90df6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNNN../da68f.. ownership of 30e15.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMExu../2c677.. ownership of 236dc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWdQ../48292.. ownership of aae2a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLeU../d7b38.. ownership of 9256b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHBc../131a0.. ownership of 1ecd5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWA1../c61ef.. ownership of 570d1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRwt../501d2.. ownership of 10cc5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRe7../f7852.. ownership of bfb39.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMG2y../87491.. ownership of 1d448.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGJb../e34ae.. ownership of a4d5d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQew../78c4d.. ownership of f9752.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKiF../08f93.. ownership of bb92b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYis../8ea0d.. ownership of 80dbd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc2J../e2309.. ownership of a6d15.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML18../e862c.. ownership of 72c39.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdeW../f0af2.. ownership of 5328d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKRV../85809.. ownership of 82110.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMb6t../0faf2.. ownership of 39736.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUjC../0990d.. ownership of 10dc7.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdot../efebd.. ownership of e1408.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRi7../e4735.. ownership of a0c85.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVxv../94bbf.. ownership of 54bb6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW6S../f66a8.. ownership of aa959.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGBz../a6c76.. ownership of 8dac9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHPJ../05926.. ownership of 40c01.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQiU../a3280.. ownership of 773c6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKHU../9a491.. ownership of f1550.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSK5../f7800.. ownership of 32b7a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHLq../e8f34.. ownership of 163bc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZZv../b47bf.. ownership of 5fe43.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQa3../6690b.. ownership of 40523.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZvk../00c21.. ownership of d57ae.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRbV../62885.. ownership of 314fa.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQow../565f8.. ownership of 67584.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRzi../c7ece.. ownership of 36521.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXK2../b6d51.. ownership of 366f9.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX5z../7bfcc.. ownership of 6e7f6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYE7../b0b1a.. ownership of e1e4a.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHGx../854c9.. ownership of e70f5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdnP../aab5c.. ownership of 36169.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTyY../01ced.. ownership of 98c79.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZid../24574.. ownership of 8fb4b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd5h../06d66.. ownership of fec92.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLa1../71f84.. ownership of af84f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQnC../649d7.. ownership of da017.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWSk../5f3b9.. ownership of a0d13.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSjW../affac.. ownership of b1546.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbpr../eaa18.. ownership of 72a49.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKqR../3313e.. ownership of fb293.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbF9../c583c.. ownership of d123b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHBi../49618.. ownership of 113d5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN4C../b0b71.. ownership of 54fcb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcLT../3599f.. ownership of dbfc3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHju../4e24e.. ownership of e93fc.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJZ9../773d3.. ownership of f5875.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVbs../1c0ca.. ownership of beda8.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHK1../489e2.. ownership of 547f6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRag../1b862.. ownership of 8c5bf.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMant../319eb.. ownership of edc0b.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcFm../01ed8.. ownership of cdd41.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTgu../b3e3a.. ownership of 61987.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMda../a79ea.. ownership of 46441.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHE9../f7831.. ownership of 01c56.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUPtm../d09d6.. doc published by PrGxv..
Param SNoSNo : ι → ο
Param add_SNoadd_SNo : ι → ι → ι
Known SNo_add_SNoSNo_add_SNo : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ SNo (add_SNo x0 x1)
Known SNo_add_SNo_4SNo_add_SNo_4 : ∀ x0 x1 x2 x3 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 x3)))
Theorem SNo_add_SNo_5SNo_add_SNo_5 : ∀ x0 x1 x2 x3 x4 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 x4)))) (proof)
Theorem SNo_add_SNo_6SNo_add_SNo_6 : ∀ x0 x1 x2 x3 x4 x5 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 x5))))) (proof)
Theorem SNo_add_SNo_7SNo_add_SNo_7 : ∀ x0 x1 x2 x3 x4 x5 x6 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 x6)))))) (proof)
Theorem SNo_add_SNo_8SNo_add_SNo_8 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 x7))))))) (proof)
Theorem SNo_add_SNo_9SNo_add_SNo_9 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 x8)))))))) (proof)
Theorem SNo_add_SNo_10SNo_add_SNo_10 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 x9))))))))) (proof)
Theorem SNo_add_SNo_11SNo_add_SNo_11 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 x10)))))))))) (proof)
Theorem SNo_add_SNo_12SNo_add_SNo_12 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x11))))))))))) (proof)
Theorem SNo_add_SNo_13SNo_add_SNo_13 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 x12)))))))))))) (proof)
Theorem SNo_add_SNo_14SNo_add_SNo_14 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 x13))))))))))))) (proof)
Theorem SNo_add_SNo_15SNo_add_SNo_15 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 x14)))))))))))))) (proof)
Theorem SNo_add_SNo_16SNo_add_SNo_16 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 x15))))))))))))))) (proof)
Theorem SNo_add_SNo_17SNo_add_SNo_17 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 x16)))))))))))))))) (proof)
Theorem SNo_add_SNo_18SNo_add_SNo_18 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 x17))))))))))))))))) (proof)
Theorem SNo_add_SNo_19SNo_add_SNo_19 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 x18)))))))))))))))))) (proof)
Theorem SNo_add_SNo_20SNo_add_SNo_20 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 x19))))))))))))))))))) (proof)
Theorem SNo_add_SNo_21SNo_add_SNo_21 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 x20)))))))))))))))))))) (proof)
Theorem SNo_add_SNo_22SNo_add_SNo_22 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 x21))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_23SNo_add_SNo_23 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 x22)))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_24SNo_add_SNo_24 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 x23))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_25SNo_add_SNo_25 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 x24)))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_26SNo_add_SNo_26 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 x25))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_27SNo_add_SNo_27 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 x26)))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_28SNo_add_SNo_28 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 x27))))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_29SNo_add_SNo_29 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 x28)))))))))))))))))))))))))))) (proof)
Theorem SNo_add_SNo_30SNo_add_SNo_30 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo x29 ⟶ SNo (add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (add_SNo x28 x29))))))))))))))))))))))))))))) (proof)
Param minus_SNominus_SNo : ι → ι
Known minus_add_SNo_distrminus_add_SNo_distr : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ minus_SNo (add_SNo x0 x1) = add_SNo (minus_SNo x0) (minus_SNo x1)
Known SNo_minus_SNoSNo_minus_SNo : ∀ x0 . SNo x0 ⟶ SNo (minus_SNo x0)
Known minus_SNo_involminus_SNo_invol : ∀ x0 . SNo x0 ⟶ minus_SNo (minus_SNo x0) = x0
Theorem minus_add_SNo_distr_mminus_add_SNo_distr_m : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ minus_SNo (add_SNo (minus_SNo x0) x1) = add_SNo x0 (minus_SNo x1) (proof)
Theorem minus_add_SNo_distr_m_2minus_add_SNo_distr_m_2 : ∀ x0 x1 x2 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) x2)) = add_SNo x0 (add_SNo x1 (minus_SNo x2)) (proof)
Theorem minus_add_SNo_distr_m_2bminus_add_SNo_distr_m_2b : ∀ x0 x1 . SNo x0 ⟶ SNo x1 ⟶ minus_SNo (add_SNo (minus_SNo x0) (minus_SNo x1)) = add_SNo x0 x1 (proof)
Theorem minus_add_SNo_distr_m_3minus_add_SNo_distr_m_3 : ∀ x0 x1 x2 x3 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) x3))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (minus_SNo x3))) (proof)
Theorem minus_add_SNo_distr_m_4minus_add_SNo_distr_m_4 : ∀ x0 x1 x2 x3 x4 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) x4)))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (minus_SNo x4)))) (proof)
Theorem minus_add_SNo_distr_m_5minus_add_SNo_distr_m_5 : ∀ x0 x1 x2 x3 x4 x5 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) x5))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (minus_SNo x5))))) (proof)
Theorem minus_add_SNo_distr_m_6minus_add_SNo_distr_m_6 : ∀ x0 x1 x2 x3 x4 x5 x6 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) x6)))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (minus_SNo x6)))))) (proof)
Theorem minus_add_SNo_distr_m_7minus_add_SNo_distr_m_7 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) x7))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (minus_SNo x7))))))) (proof)
Theorem minus_add_SNo_distr_m_8minus_add_SNo_distr_m_8 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) x8)))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (minus_SNo x8)))))))) (proof)
Theorem minus_add_SNo_distr_m_9minus_add_SNo_distr_m_9 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) x9))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (minus_SNo x9))))))))) (proof)
Theorem minus_add_SNo_distr_m_10minus_add_SNo_distr_m_10 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) x10)))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (minus_SNo x10)))))))))) (proof)
Theorem minus_add_SNo_distr_m_11minus_add_SNo_distr_m_11 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) x11))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (minus_SNo x11))))))))))) (proof)
Theorem minus_add_SNo_distr_m_12minus_add_SNo_distr_m_12 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) x12)))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (minus_SNo x12)))))))))))) (proof)
Theorem minus_add_SNo_distr_m_13minus_add_SNo_distr_m_13 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) x13))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (minus_SNo x13))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_14minus_add_SNo_distr_m_14 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) x14)))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (minus_SNo x14)))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_15minus_add_SNo_distr_m_15 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) x15))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (minus_SNo x15))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_16minus_add_SNo_distr_m_16 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) x16)))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (minus_SNo x16)))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_17minus_add_SNo_distr_m_17 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) x17))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (minus_SNo x17))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_18minus_add_SNo_distr_m_18 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) x18)))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (minus_SNo x18)))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_19minus_add_SNo_distr_m_19 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) x19))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (minus_SNo x19))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_20minus_add_SNo_distr_m_20 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) x20)))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (minus_SNo x20)))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_21minus_add_SNo_distr_m_21 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) x21))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (minus_SNo x21))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_22minus_add_SNo_distr_m_22 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) x22)))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (minus_SNo x22)))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_23minus_add_SNo_distr_m_23 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) x23))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (minus_SNo x23))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_24minus_add_SNo_distr_m_24 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) x24)))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (minus_SNo x24)))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_25minus_add_SNo_distr_m_25 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) x25))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (minus_SNo x25))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_26minus_add_SNo_distr_m_26 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) x26)))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (minus_SNo x26)))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_27minus_add_SNo_distr_m_27 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) x27))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (minus_SNo x27))))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_28minus_add_SNo_distr_m_28 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) (add_SNo (minus_SNo x27) x28)))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (minus_SNo x28)))))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_29minus_add_SNo_distr_m_29 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo x29 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) (add_SNo (minus_SNo x27) (add_SNo (minus_SNo x28) x29))))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (add_SNo x28 (minus_SNo x29))))))))))))))))))))))))))))) (proof)
Theorem minus_add_SNo_distr_m_30minus_add_SNo_distr_m_30 : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 . SNo x0 ⟶ SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNo x5 ⟶ SNo x6 ⟶ SNo x7 ⟶ SNo x8 ⟶ SNo x9 ⟶ SNo x10 ⟶ SNo x11 ⟶ SNo x12 ⟶ SNo x13 ⟶ SNo x14 ⟶ SNo x15 ⟶ SNo x16 ⟶ SNo x17 ⟶ SNo x18 ⟶ SNo x19 ⟶ SNo x20 ⟶ SNo x21 ⟶ SNo x22 ⟶ SNo x23 ⟶ SNo x24 ⟶ SNo x25 ⟶ SNo x26 ⟶ SNo x27 ⟶ SNo x28 ⟶ SNo x29 ⟶ SNo x30 ⟶ minus_SNo (add_SNo (minus_SNo x0) (add_SNo (minus_SNo x1) (add_SNo (minus_SNo x2) (add_SNo (minus_SNo x3) (add_SNo (minus_SNo x4) (add_SNo (minus_SNo x5) (add_SNo (minus_SNo x6) (add_SNo (minus_SNo x7) (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (add_SNo (minus_SNo x19) (add_SNo (minus_SNo x20) (add_SNo (minus_SNo x21) (add_SNo (minus_SNo x22) (add_SNo (minus_SNo x23) (add_SNo (minus_SNo x24) (add_SNo (minus_SNo x25) (add_SNo (minus_SNo x26) (add_SNo (minus_SNo x27) (add_SNo (minus_SNo x28) (add_SNo (minus_SNo x29) x30)))))))))))))))))))))))))))))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 (add_SNo x21 (add_SNo x22 (add_SNo x23 (add_SNo x24 (add_SNo x25 (add_SNo x26 (add_SNo x27 (add_SNo x28 (add_SNo x29 (minus_SNo x30)))))))))))))))))))))))))))))) (proof)