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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιιο be given.
Let x3 of type ιιο be given.
Let x4 of type ιο be given.
Let x5 of type ιο be given.
Assume H0: 42836.. x0 x2 x4 = 42836.. x1 x3 x5.
Claim L1: x1 = f482f.. (42836.. x0 x2 x4) 4a7ef..
Apply unknownprop_a0c1cfbe827e15400df973a6e68533df2c6a861774fe22bb87a9ee4680d54108 with 42836.. x0 x2 x4, x1, x3, x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_59ca09c0fd122f786673713c0642ed4ce1a31aabde53a2b0a8368edd8a739e79 with x0, x2, x4.
Apply and3I with x0 = x1, ∀ x6 . prim1 x6 x0∀ x7 . prim1 x7 x0x2 x6 x7 = x3 x6 x7, ∀ x6 . prim1 x6 x0x4 x6 = x5 x6 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Assume H3: prim1 x6 x0.
Let x7 of type ι be given.
Assume H4: prim1 x7 x0.
Apply unknownprop_f9bb039047c575715dfc8b1b59b7b8ec67d811cbe7fb1bdb245069e08439d0a7 with x0, x2, x4, x6, x7, λ x8 x9 : ο . x9 = x3 x6 x7 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Claim L5: prim1 x6 x1
Apply L2 with λ x8 x9 . prim1 x6 x8.
The subproof is completed by applying H3.
Claim L6: prim1 x7 x1
Apply L2 with λ x8 x9 . prim1 x7 x8.
The subproof is completed by applying H4.
Apply H0 with λ x8 x9 . 2b2e3.. (f482f.. x9 (4ae4a.. 4a7ef..)) x6 x7 = x3 x6 x7.
Let x8 of type οοο be given.
Apply unknownprop_f9bb039047c575715dfc8b1b59b7b8ec67d811cbe7fb1bdb245069e08439d0a7 with x1, x3, x5, x6, x7, λ x9 x10 : ο . x8 x10 x9 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L6.
Let x6 of type ι be given.
Assume H3: prim1 x6 x0.
Apply unknownprop_ccbf64b584877a997f6d8dee90614a29efc1b9f302b847ac9596ce2d25fc4cd2 with x0, x2, x4, x6, λ x7 x8 : ο . x8 = x5 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Claim L4: prim1 x6 x1
Apply L2 with λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with λ x7 x8 . decode_p (f482f.. x8 (4ae4a.. (4ae4a.. 4a7ef..))) x6 = x5 x6.
Let x7 of type οοο be given.
Apply unknownprop_ccbf64b584877a997f6d8dee90614a29efc1b9f302b847ac9596ce2d25fc4cd2 with x1, x3, x5, x6, λ x8 x9 : ο . x7 x9 x8.
The subproof is completed by applying L4.