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Proofgold Signed Transaction

vin
Pr7Mr../77fa1..
PUSz3../eae21..
vout
Pr7Mr../2c9be.. 9.80 bars
TMY9W../0733b.. ownership of a62e2.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMLoZ../185d7.. ownership of f9553.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMVgB../0b5ae.. ownership of 02b3e.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMUTB../87c6b.. ownership of 0faa6.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMdUe../e532e.. ownership of a1573.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMc55../1c38e.. ownership of 9650c.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMTo1../25671.. ownership of cf2be.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMaij../17b7d.. ownership of fa6b8.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMUjR../2aa3a.. ownership of 16311.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMT7D../f3e9d.. ownership of 4cbb4.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNvP../feab1.. ownership of 41364.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMd2n../985bb.. ownership of 2bfb1.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMZw1../ff221.. ownership of 03386.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMcTv../8e35a.. ownership of 20040.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMFqm../4df62.. ownership of acc69.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMWeJ../ed88c.. ownership of ac6fe.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMa6u../f1466.. ownership of d4606.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMYze../00ae4.. ownership of 80003.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMJWX../61e23.. ownership of fddcf.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMJmL../69d75.. ownership of 5c1c6.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMUoV../3d982.. ownership of 99ded.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMJgW../f26df.. ownership of fc293.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMaJg../95157.. ownership of fc1b7.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMU4W../e096b.. ownership of 34e78.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMSXs../94f39.. ownership of 69284.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMa62../f64e8.. ownership of 670bc.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMHUX../45da2.. ownership of e7591.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TManu../11d2d.. ownership of c0b20.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNMs../1c51b.. ownership of fb450.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMYQS../24553.. ownership of f2604.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMa4f../109ab.. ownership of 58d06.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMGjS../d519d.. ownership of 41def.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMWtS../5fe6b.. ownership of 2f2ce.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMYPn../375de.. ownership of eedb2.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMGLc../64f94.. ownership of 9e914.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNhZ../d23ac.. ownership of 2c2b6.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMdhc../6aaef.. ownership of 2b177.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMXEe../6a882.. ownership of cb22f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMV32../8c497.. ownership of 7bb3f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMFAX../21d23.. ownership of ae47a.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMT4Z../c7785.. ownership of ce88f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMWY3../97494.. ownership of f632f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMRUc../d6d8d.. ownership of f2877.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMaK2../90e00.. ownership of 1e100.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMZ81../116a8.. ownership of 62991.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNLv../356e7.. ownership of c9d20.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMc96../6779a.. ownership of 6d362.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNWX../f4f8c.. ownership of 8f2a1.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMUJP../d3e4e.. ownership of 53f67.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMUzf../90e1f.. ownership of 7f383.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMZSH../d4f92.. ownership of 74cfe.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMPZ1../74401.. ownership of e035c.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMYLa../e03fd.. ownership of a2e43.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNnm../46cf8.. ownership of 349db.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMSFD../ad93d.. ownership of b2788.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMJRG../74eb2.. ownership of 1a52e.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMTSM../b7f91.. ownership of 2b6ba.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMQ1g../e6de9.. ownership of 5085c.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMZ9L../4d8ac.. ownership of c83a0.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMbNj../79b18.. ownership of 5e262.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMYsu../6110d.. ownership of 9814f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMMmv../38f55.. ownership of c6a33.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMT4T../540ef.. ownership of 07519.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMKpH../e41cd.. ownership of a28d7.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMF6B../c0515.. ownership of 0ac77.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMSCK../7526c.. ownership of b1346.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMFhR../2c189.. ownership of 5af12.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMQzm../cfac3.. ownership of 73c08.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMRVt../b93de.. ownership of 63495.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMW2w../495ba.. ownership of ce01d.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMPuN../2d5db.. ownership of e6b7d.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMPY7../2a7d5.. ownership of 413f8.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMHFF../5bc4d.. ownership of f429f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMMWc../6c970.. ownership of f1b4b.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMapw../c7bdf.. ownership of 224e2.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMFYG../b3902.. ownership of ace71.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMQiR../db25f.. ownership of d6dd4.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMEt5../19ba6.. ownership of 2cd90.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMWa3../14ddb.. ownership of 4c6ff.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMJPw../aefc8.. ownership of 23bcc.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMMuY../7893b.. ownership of 06adb.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMNSK../15401.. ownership of c5984.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMU8h../40d57.. ownership of 7928f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMXAi../1cc7c.. ownership of ea7b2.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMVn1../4a219.. ownership of 060d0.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMdWv../79296.. ownership of 32e4f.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMdCP../919fe.. ownership of f186e.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMZ67../1fd90.. ownership of 8c657.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMYZz../3a30a.. ownership of 2fe73.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMTUR../86fed.. ownership of 62108.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMU5k../d9e24.. ownership of 2931a.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMRtD../a7f71.. ownership of a57c5.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMXDL../0872e.. ownership of a84bb.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
TMUF5../87f06.. ownership of 8bc85.. as prop with payaddr PrBPC.. rightscost 0.00 controlledby PrBPC.. upto 0
PUaSf../a53bf.. doc published by PrBPC..
Known 429a0..equip_mod_I1 : ∀ x0 x1 x2 x3 x4 . equip (setsum x0 x3) x1 ⟶ equip (setprod x4 x3) x2 ⟶ equip_mod x0 x1 x2
Known 30edc..equip_tra : ∀ x0 x1 x2 . equip x0 x1 ⟶ equip x1 x2 ⟶ equip x0 x2
Known 637fd..equip_sym : ∀ x0 x1 . equip x0 x1 ⟶ equip x1 x0
Known c9b7c..equipE_impred : ∀ x0 x1 . equip x0 x1 ⟶ ∀ x2 : ο . (∀ x3 : ι → ι . bij x0 x1 x3 ⟶ x2) ⟶ x2
Known 80a11..bijE_impred : ∀ x0 x1 . ∀ x2 : ι → ι . bij x0 x1 x2 ⟶ ∀ x3 : ο . (inj x0 x1 x2 ⟶ (∀ x4 . In x4 x1 ⟶ ∀ x5 : ο . (∀ x6 . and (In x6 x0) (x2 x6 = x4) ⟶ x5) ⟶ x5) ⟶ x3) ⟶ x3
Known e6daf..injE_impred : ∀ x0 x1 . ∀ x2 : ι → ι . inj x0 x1 x2 ⟶ ∀ x3 : ο . ((∀ x4 . In x4 x0 ⟶ In (x2 x4) x1) ⟶ (∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 x0 ⟶ x2 x4 = x2 x5 ⟶ x4 = x5) ⟶ x3) ⟶ x3
Known f2c5c..equipI : ∀ x0 x1 . ∀ x2 : ι → ι . bij x0 x1 x2 ⟶ equip x0 x1
Known e5c63..bijI : ∀ x0 x1 . ∀ x2 : ι → ι . inj x0 x1 x2 ⟶ (∀ x3 . In x3 x1 ⟶ ∀ x4 : ο . (∀ x5 . and (In x5 x0) (x2 x5 = x3) ⟶ x4) ⟶ x4) ⟶ bij x0 x1 x2
Known 1796e..injI : ∀ x0 x1 . ∀ x2 : ι → ι . (∀ x3 . In x3 x0 ⟶ In (x2 x3) x1) ⟶ (∀ x3 . In x3 x0 ⟶ ∀ x4 . In x4 x0 ⟶ x2 x3 = x2 x4 ⟶ x3 = x4) ⟶ inj x0 x1 x2
Known b4776..ordsuccE_impred : ∀ x0 x1 . In x1 (ordsucc x0) ⟶ ∀ x2 : ο . (In x1 x0 ⟶ x2) ⟶ (x1 = x0 ⟶ x2) ⟶ x2
Known 0d2f9..If_i_1 : ∀ x0 : ο . ∀ x1 x2 . x0 ⟶ If_i x0 x1 x2 = x1
Known 93236..Inj0_setsum : ∀ x0 x1 x2 . In x2 x0 ⟶ In (Inj0 x2) (setsum x0 x1)
Known 81513..If_i_0 : ∀ x0 : ο . ∀ x1 x2 . not x0 ⟶ If_i x0 x1 x2 = x2
Known 9ea3e..Inj1_setsum : ∀ x0 x1 x2 . In x2 x1 ⟶ In (Inj1 x2) (setsum x0 x1)
Known 0978b..In_0_1 : In 0 1
Known 49afe..Inj0_inj : ∀ x0 x1 . Inj0 x0 = Inj0 x1 ⟶ x0 = x1
Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0
Known notEnotE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ False
Known efcec..Inj0_Inj1_neq : ∀ x0 x1 . not (Inj0 x0 = Inj1 x1)
Known 26db0..setsum_def : setsum = λ x1 x2 . binunion (Repl x1 Inj0) (Repl x2 Inj1)
Known f9974..binunionE_cases : ∀ x0 x1 x2 . In x2 (binunion x0 x1) ⟶ ∀ x3 : ο . (In x2 x0 ⟶ x3) ⟶ (In x2 x1 ⟶ x3) ⟶ x3
Known 0f096..ReplE2 : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . In x2 (Repl x0 x1) ⟶ ∀ x3 : ο . (∀ x4 . In x4 x0 ⟶ x2 = x1 x4 ⟶ x3) ⟶ x3
Known andEandE : ∀ x0 x1 : ο . and x0 x1 ⟶ ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2
Known 7c02f..andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Known e9b50..ordsuccI1b : ∀ x0 x1 . In x1 x0 ⟶ In x1 (ordsucc x0)
Known cf025..ordsuccI2 : ∀ x0 . In x0 (ordsucc x0)
Known e51a8..cases_1 : ∀ x0 . In x0 1 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 x0
Known 681fa..proj0_setprod : ∀ x0 x1 x2 . In x2 (setprod x0 x1) ⟶ In (proj0 x2) x0
Known c1504..tuple_setprod_eta : ∀ x0 x1 x2 . In x2 (setprod x0 x1) ⟶ lam 2 (λ x4 . If_i (x4 = 0) (ap x2 0) (ap x2 1)) = x2
Known 82f37..proj0_ap_0 : ∀ x0 . proj0 x0 = ap x0 0
Known 9ae18..SingE : ∀ x0 x1 . In x1 (Sing x0) ⟶ x1 = x0
Known 5c344..eq_1_Sing0 : 1 = Sing 0
Known 6789e..ap1_setprod : ∀ x0 x1 x2 . In x2 (setprod x0 x1) ⟶ In (ap x2 1) x1
Known 07808..pair_setprod : ∀ x0 x1 x2 . In x2 x0 ⟶ ∀ x3 . In x3 x1 ⟶ In (setsum x2 x3) (setprod x0 x1)
Known d6e1a..proj0_pair_eq : ∀ x0 x1 . proj0 (setsum x0 x1) = x0
Known 8106d..notI : ∀ x0 : ο . (x0 ⟶ False) ⟶ not x0
Known 2a3a3..In_irref_b : ∀ x0 . In x0 x0 ⟶ False
Theorem a84bb.. : ∀ x0 x1 x2 x3 . equip x0 x3 ⟶ equip x1 (ordsucc x3) ⟶ equip_mod x0 x1 x2 (proof)
Known dd0ac..equip_mod_I2 : ∀ x0 x1 x2 x3 x4 . equip (setsum x1 x3) x0 ⟶ equip (setprod x4 x3) x2 ⟶ equip_mod x0 x1 x2
Theorem 2931a.. : ∀ x0 x1 x2 x3 . equip x0 (ordsucc x3) ⟶ equip x1 x3 ⟶ equip_mod x0 x1 x2 (proof)
Known 2901c..EmptyE : ∀ x0 . In x0 0 ⟶ False
Known bc2f0..ap_setexp : ∀ x0 x1 x2 . In x2 (setexp x1 x0) ⟶ ∀ x3 . In x3 x0 ⟶ In (ap x2 x3) x1
Theorem 2fe73.. : ∀ x0 x1 . In x1 x0 ⟶ equip (setexp 0 x0) 0 (proof)
Known eead0..setexp_ext : ∀ x0 x1 x2 . In x2 (setexp x1 x0) ⟶ ∀ x3 . In x3 (setexp x1 x0) ⟶ (∀ x4 . In x4 x0 ⟶ ap x2 x4 = ap x3 x4) ⟶ x2 = x3
Known 3152e..lam_setexp : ∀ x0 x1 . ∀ x2 : ι → ι . (∀ x3 . In x3 x0 ⟶ In (x2 x3) x1) ⟶ In (lam x0 x2) (setexp x1 x0)
Theorem f186e.. : ∀ x0 . equip (setexp 1 x0) 1 (proof)
Param 69aae..exp_nat : ι → ι → ι
Known d5467..equip_setexp_ordsucc_setprod : ∀ x0 x1 . equip (setexp x1 (ordsucc x0)) (setprod x1 (setexp x1 x0))
Known f4890..exp_nat_S : ∀ x0 x1 . nat_p x1 ⟶ 69aae.. x0 (ordsucc x1) = mul_nat x0 (69aae.. x0 x1)
Known 912b9..equip_setprod_mul_nat_2 : ∀ x0 . nat_p x0 ⟶ ∀ x1 . nat_p x1 ⟶ ∀ x2 x3 . equip x2 x0 ⟶ equip x3 x1 ⟶ equip (setprod x2 x3) (mul_nat x0 x1)
Known 2f247..exp_nat_p : ∀ x0 . nat_p x0 ⟶ ∀ x1 . nat_p x1 ⟶ nat_p (69aae.. x0 x1)
Known 21472..equip_setexp_3 : ∀ x0 . nat_p x0 ⟶ ∀ x1 . equip x1 x0 ⟶ equip (setexp x1 3) (69aae.. x0 3)
Known 21479..nat_ordsucc : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc x0)
Known 36841..nat_2 : nat_p 2
Theorem 060d0.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 . equip x1 x0 ⟶ equip (setexp x1 4) (69aae.. x0 4) (proof)
Known fa8b5..Sep_In_Power : ∀ x0 . ∀ x1 : ι → ο . In (Sep x0 x1) (Power x0)
Known 3ad28..cases_2 : ∀ x0 . In x0 2 ⟶ ∀ x1 : ι → ο . x1 0 ⟶ x1 1 ⟶ x1 x0
Known dab1f..SepI : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . In x2 x0 ⟶ x1 x2 ⟶ In x2 (Sep x0 x1)
Known e3ec9..neq_0_1 : not (0 = 1)
Known 076ba..SepE2 : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . In x2 (Sep x0 x1) ⟶ x1 x2
Known 47706..xmcases : ∀ x0 x1 : ο . (x0 ⟶ x1) ⟶ (not x0 ⟶ x1) ⟶ x1
Known 0a117..In_1_2 : In 1 2
Known 0863e..In_0_2 : In 0 2
Known 535f2..set_ext_2 : ∀ x0 x1 . (∀ x2 . In x2 x0 ⟶ In x2 x1) ⟶ (∀ x2 . In x2 x1 ⟶ In x2 x0) ⟶ x0 = x1
Known b4782..contra : ∀ x0 : ο . (not x0 ⟶ False) ⟶ x0
Known aa3f4..SepE_impred : ∀ x0 . ∀ x1 : ι → ο . ∀ x2 . In x2 (Sep x0 x1) ⟶ ∀ x3 : ο . (In x2 x0 ⟶ x1 x2 ⟶ x3) ⟶ x3
Known b515a..beta : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . In x2 x0 ⟶ ap (lam x0 x1) x2 = x1 x2
Known decfb..PowerE2 : ∀ x0 x1 . In x1 (Power x0) ⟶ ∀ x2 . In x2 x1 ⟶ In x2 x0
Theorem 7928f.. : ∀ x0 . equip (setexp 2 x0) (Power x0) (proof)
Known e8081..tuple_2_setprod : ∀ x0 x1 x2 . In x2 x0 ⟶ ∀ x3 . In x3 x1 ⟶ In (lam 2 (λ x4 . If_i (x4 = 0) x2 x3)) (setprod x0 x1)
Known 54d83..setminusE1 : ∀ x0 x1 x2 . In x2 (setminus x0 x1) ⟶ In x2 x0
Known abe40..tuple_2_inj_impred : ∀ x0 x1 x2 x3 . lam 2 (λ x5 . If_i (x5 = 0) x0 x1) = lam 2 (λ x5 . If_i (x5 = 0) x2 x3) ⟶ ∀ x4 : ο . (x0 = x2 ⟶ x1 = x3 ⟶ x4) ⟶ x4
Known 626dc..setminusI : ∀ x0 x1 x2 . In x2 x0 ⟶ nIn x2 x1 ⟶ In x2 (setminus x0 x1)
Known 9d2e6..nIn_I2 : ∀ x0 x1 . (In x0 x1 ⟶ False) ⟶ nIn x0 x1
Known 24526..nIn_E2 : ∀ x0 x1 . nIn x0 x1 ⟶ In x0 x1 ⟶ False
Known 28403..setminusE2 : ∀ x0 x1 x2 . In x2 (setminus x0 x1) ⟶ nIn x2 x1
Known 1f15b..SingI : ∀ x0 . In x0 (Sing x0)
Known fe28a..ap0_setprod : ∀ x0 x1 x2 . In x2 (setprod x0 x1) ⟶ In (ap x2 0) x0
Theorem 06adb.. : ∀ x0 x1 x2 . In x2 x1 ⟶ equip (setexp x0 x1) (setprod x0 (setexp x0 (setminus x1 (Sing x2)))) (proof)
Known d0de4..Empty_eq : ∀ x0 . (∀ x1 . nIn x1 x0) ⟶ x0 = 0
Theorem 82600.. : ∀ x0 . equip x0 0 ⟶ x0 = 0 (proof)
Known fed08..nat_ind : ∀ x0 : ι → ο . x0 0 ⟶ (∀ x1 . nat_p x1 ⟶ x0 x1 ⟶ x0 (ordsucc x1)) ⟶ ∀ x1 . nat_p x1 ⟶ x0 x1
Known 94de7..exp_nat_0 : ∀ x0 . 69aae.. x0 0 = 1
Theorem 4c6ff.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 . nat_p x1 ⟶ ∀ x2 x3 . equip x2 x0 ⟶ equip x3 x1 ⟶ equip (setexp x2 x3) (69aae.. x0 x1) (proof)
Known 5fc88..binrep_def : binrep = λ x1 x2 . setsum x1 (Power x2)
Known 56707..equip_setsum_add_nat_2 : ∀ x0 . nat_p x0 ⟶ ∀ x1 . nat_p x1 ⟶ ∀ x2 x3 . equip x2 x0 ⟶ equip x3 x1 ⟶ equip (setsum x2 x3) (add_nat x0 x1)
Known 54d4b..equip_ref : ∀ x0 . equip x0 x0
Theorem d6dd4.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 . nat_p x1 ⟶ ∀ x2 x3 . equip x2 x0 ⟶ equip x3 x1 ⟶ equip (binrep x2 x3) (add_nat x0 (69aae.. 2 x1)) (proof)
Known 08405..nat_0 : nat_p 0
Theorem 224e2.. : ∀ x0 . equip x0 0 ⟶ equip (Power x0) 1 (proof)
Known 9b388..mul_nat_1R : ∀ x0 . mul_nat x0 1 = x0
Theorem f429f.. : 69aae.. 2 1 = 2 (proof)
Known c7c31..nat_1 : nat_p 1
Theorem e6b7d.. : ∀ x0 . equip x0 1 ⟶ equip (Power x0) 2 (proof)
Known c13d1..add_nat_SR : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc x1) = ordsucc (add_nat x0 x1)
Known 02169..add_nat_0R : ∀ x0 . add_nat x0 0 = x0
Theorem 63495.. : ∀ x0 . add_nat x0 1 = ordsucc x0 (proof)
Theorem 5af12.. : ∀ x0 . add_nat x0 2 = ordsucc (ordsucc x0) (proof)
Theorem 0ac77.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc x1)) = ordsucc (ordsucc (add_nat x0 x1)) (proof)
Theorem 07519.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc x0)) (proof)
Theorem 9814f.. : nat_p 3 (proof)
Theorem c83a0.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc x0)))) (proof)
Theorem 2b6ba.. : nat_p 4 (proof)
Theorem b2788.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))) (proof)
Theorem a2e43.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))) (proof)
Theorem 74cfe.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))))))))))))))))))) (proof)
Theorem 53f67.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem 6d362.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem 62991.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem f2877.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem ce88f.. : ∀ x0 . nat_p x0 ⟶ nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem 7bb3f.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc x1)))) = ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))) (proof)
Theorem 2b177.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))) (proof)
Theorem 9e914.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))))))))))) (proof)
Theorem 2f2ce.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))))))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))))))))))))))))))))))))))) (proof)
Theorem 58d06.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem fb450.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem e7591.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem 69284.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (proof)
Theorem fc1b7.. : ∀ x0 x1 . nat_p x1 ⟶ add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc 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(proof)
Known a6e5c..mul_nat_SR : ∀ x0 x1 . nat_p x1 ⟶ mul_nat x0 (ordsucc x1) = add_nat x0 (mul_nat x0 x1)
Theorem 99ded.. : mul_nat 2 2 = 4 (proof)
Theorem fddcf.. : 69aae.. 2 2 = 4 (proof)
Theorem d4606.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 x2 . equip x1 x0 ⟶ equip x2 0 ⟶ equip (binrep x1 x2) (ordsucc x0) (proof)
Theorem acc69.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 x2 . equip x1 x0 ⟶ equip x2 1 ⟶ equip (binrep x1 x2) (ordsucc (ordsucc x0)) (proof)
Theorem 03386.. : ∀ x0 . nat_p x0 ⟶ ∀ x1 x2 . equip x1 x0 ⟶ equip x2 2 ⟶ equip (binrep x1 x2) (ordsucc (ordsucc (ordsucc (ordsucc x0)))) (proof)
Known 26d71..add_nat_1_1_2 : add_nat 1 1 = 2
Known d18f8..mul_add_nat_distrR : ∀ x0 . nat_p x0 ⟶ ∀ x1 . nat_p x1 ⟶ ∀ x2 . nat_p x2 ⟶ mul_nat (add_nat x0 x1) x2 = add_nat (mul_nat x0 x2) (mul_nat x1 x2)
Known e6942..mul_nat_1L : ∀ x0 . nat_p x0 ⟶ mul_nat 1 x0 = x0
Theorem 41364.. : ∀ x0 . nat_p x0 ⟶ mul_nat 2 x0 = add_nat x0 x0 (proof)
Theorem 16311.. : 69aae.. 2 3 = 8 (proof)
Theorem cf2be.. : 69aae.. 2 4 = 16 (proof)
Theorem a1573.. : ∀ x0 . equip x0 2 ⟶ equip (Power x0) 4 (proof)
Theorem 02b3e.. : ∀ x0 . equip x0 3 ⟶ equip (Power x0) 8 (proof)
Theorem a62e2.. : ∀ x0 . equip x0 4 ⟶ equip (Power x0) 16 (proof)