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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Apply unknownprop_9846a3b9b296163e6b61794e26bc3e26fa2fbe6bf441b272a5bec41a167f1c0b with ad280.. x0 x1, 28f8d.. (ad280.. x0 x1) = x0 leaving 2 subgoals.
Apply unknownprop_942959aad6790cf3a71a2f8f2b9ffc552b42fb28a7f163a4f5e7e7842fdbd934 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: SNo (28f8d.. (ad280.. x0 x1)).
Assume H3: ∃ x2 . and (SNo x2) (ad280.. x0 x1 = ad280.. (28f8d.. (ad280.. x0 x1)) x2).
Apply H3 with 28f8d.. (ad280.. x0 x1) = x0.
Let x2 of type ι be given.
Assume H4: (λ x3 . and (SNo x3) (ad280.. x0 x1 = ad280.. (28f8d.. (ad280.. x0 x1)) x3)) x2.
Apply H4 with 28f8d.. (ad280.. x0 x1) = x0.
Assume H5: SNo x2.
Assume H6: ad280.. x0 x1 = ad280.. (28f8d.. (ad280.. x0 x1)) x2.
Let x3 of type ι → ι → ο be given.
Apply unknownprop_91df53020fea6a9ff4cc6802b4e01884637366fdcf8bc35cea3e79e3c777050d with x0, x1, 28f8d.. (ad280.. x0 x1), x2, λ x4 x5 . x3 x5 x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H6.
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