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Proofgold Signed Transaction

vin
PrAmQ../93dc4..
PUZkj../8ba65..
vout
PrAmQ../c423f.. 9.97 bars
TML5i../d0d36.. ownership of 212cb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSwy../16251.. ownership of 90461.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQvZ../14aee.. ownership of b09b1.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ4F../1edeb.. ownership of a0d0c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJxD../1796d.. ownership of 0ceda.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMcQJ../14bc5.. ownership of 54751.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaco../6bc7f.. ownership of e19f0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZ89../4d3ae.. ownership of d526c.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdKc../d73e2.. ownership of bd5cb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVG7../ab36d.. ownership of 9c093.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXqd../5ecd8.. ownership of ddf23.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPSR../c7fe9.. ownership of 033fb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMM5h../469cd.. ownership of 6bdd5.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN1F../1288b.. ownership of db83f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUJA../2ffa2.. ownership of edf3f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWf1../4ac22.. ownership of 31582.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML2C../4309a.. ownership of 83b97.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXbM../afb85.. ownership of d2a56.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRCE../32654.. ownership of 98497.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNmy../29bc3.. ownership of d2249.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXwN../6a2e1.. ownership of 2df14.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJCB../86cee.. ownership of 12211.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPXY../3f400.. ownership of 5c2dd.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKP8../5a4ce.. ownership of fcc70.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJXx../75b68.. ownership of 04e57.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWfv../dbb42.. ownership of 44edb.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZih../35a98.. ownership of 0eec3.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJq9../1223b.. ownership of 76236.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbmB../5596e.. ownership of ce37f.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMX3L../830c9.. ownership of c897d.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQrn../d35e6.. ownership of 96508.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdQY../85bc1.. ownership of 875f6.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJnC../c2ce4.. ownership of 5e6e0.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYUS../15011.. ownership of 750a4.. as prop with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUfT1../b471c.. doc published by PrGxv..
Param f482f.. : ι → ι → ι
Param 0fc90.. : ι → (ι → ι) → ι
Param 4ae4a.. : ι → ι
Param 4a7ef.. : ι
Param If_i : ο → ι → ι → ι
Known f22ec.. : ∀ x0 . ∀ x1 : ι → ι . ∀ x2 . prim1 x2 x0 ⟶ f482f.. (0fc90.. x0 x1) x2 = x1 x2
Known 06ef3.. : prim1 4a7ef.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known If_i_1 : ∀ x0 : ο . ∀ x1 x2 . x0 ⟶ If_i x0 x1 x2 = x1
Theorem 5e6e0.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) 4a7ef.. = x0 (proof)
Known 71150.. : prim1 (4ae4a.. 4a7ef..) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Definition False := ∀ x0 : ο . x0
Definition not := λ x0 : ο . x0 ⟶ False
Known If_i_0 : ∀ x0 : ο . ∀ x1 x2 . not x0 ⟶ If_i x0 x1 x2 = x2
Known 5c667.. : 4ae4a.. 4a7ef.. = 4a7ef.. ⟶ ∀ x0 : ο . x0
Theorem 96508.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. 4a7ef..) = x1 (proof)
Known 49aa4.. : prim1 (4ae4a.. (4ae4a.. 4a7ef..)) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known 3a2b6.. : 4ae4a.. (4ae4a.. 4a7ef..) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known f9d2f.. : 4ae4a.. (4ae4a.. 4a7ef..) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Theorem ce37f.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. (4ae4a.. 4a7ef..)) = x2 (proof)
Known caeb5.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known 57b7e.. : 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known daead.. : 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 0c325.. : 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) = 4ae4a.. (4ae4a.. 4a7ef..) ⟶ ∀ x0 : ο . x0
Theorem 0eec3.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x3 (proof)
Known d4e8e.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known 37f0a.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known d1b49.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 05e02.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = 4ae4a.. (4ae4a.. 4a7ef..) ⟶ ∀ x0 : ο . x0
Known 2f510.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) ⟶ ∀ x0 : ο . x0
Theorem 04e57.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x4 (proof)
Known 69e64.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known 3dae7.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known a82a2.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 7fa57.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = 4ae4a.. (4ae4a.. 4a7ef..) ⟶ ∀ x0 : ο . x0
Known 67cbd.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) ⟶ ∀ x0 : ο . x0
Known e25a7.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) ⟶ ∀ x0 : ο . x0
Theorem 5c2dd.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x5 (proof)
Known 4b5d5.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known cdcd4.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 31e4d.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 5ccd2.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. 4a7ef..) ⟶ ∀ x0 : ο . x0
Known 7357c.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) ⟶ ∀ x0 : ο . x0
Known d13e3.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) ⟶ ∀ x0 : ο . x0
Known 2d896.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) ⟶ ∀ x0 : ο . x0
Theorem 2df14.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = x6 (proof)
Known cbdee.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))
Known ecc01.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known c6805.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 58158.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4ae4a.. (4ae4a.. 4a7ef..) ⟶ ∀ x0 : ο . x0
Known 16901.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) ⟶ ∀ x0 : ο . x0
Known ee53e.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) ⟶ ∀ x0 : ο . x0
Known ac13b.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) ⟶ ∀ x0 : ο . x0
Known 516c5.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) ⟶ ∀ x0 : ο . x0
Theorem 98497.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (λ x9 . If_i (x9 = 4a7ef..) x0 (If_i (x9 = 4ae4a.. 4a7ef..) x1 (If_i (x9 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x9 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 x7)))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = x7 (proof)
Known 1cd68.. : prim1 4a7ef.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem 83b97.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) 4a7ef.. = x0 (proof)
Known 4e80f.. : prim1 (4ae4a.. 4a7ef..) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem edf3f.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. 4a7ef..) = x1 (proof)
Known 384d5.. : prim1 (4ae4a.. (4ae4a.. 4a7ef..)) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem 6bdd5.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. 4a7ef..)) = x2 (proof)
Known c8b62.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem ddf23.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) = x3 (proof)
Known 1ebb9.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem bd5cb.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x4 (proof)
Known 9bb00.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem e19f0.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x5 (proof)
Known 0d93c.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem 0ceda.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = x6 (proof)
Known 65954.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Theorem b09b1.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = x7 (proof)
Known a1e1a.. : prim1 (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))))
Known 58716.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 19797.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. 4a7ef.. ⟶ ∀ x0 : ο . x0
Known 8fcc8.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. (4ae4a.. 4a7ef..) ⟶ ∀ x0 : ο . x0
Known f5d01.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)) ⟶ ∀ x0 : ο . x0
Known 622d4.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) ⟶ ∀ x0 : ο . x0
Known 17be6.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) ⟶ ∀ x0 : ο . x0
Known cc164.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) ⟶ ∀ x0 : ο . x0
Known c4f4e.. : 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) ⟶ ∀ x0 : ο . x0
Theorem 212cb.. : ∀ x0 x1 x2 x3 x4 x5 x6 x7 x8 . f482f.. (0fc90.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))))) (λ x10 . If_i (x10 = 4a7ef..) x0 (If_i (x10 = 4ae4a.. 4a7ef..) x1 (If_i (x10 = 4ae4a.. (4ae4a.. 4a7ef..)) x2 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))) x3 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) x4 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) x5 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) x6 (If_i (x10 = 4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))))) x7 x8))))))))) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))))) = x8 (proof)