Proof step e-c628eede86362da4

basis_map_theorem → concludes about Triangle read by rows: T(n, k) = T(n-1, k-1) - T(n-2, k), with T(n, n) = 1, T(n, n-1) = -2. JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Basis map theorem for the node's own rule

{
  "operation": "basis_map_theorem"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "basis_map_preserver", "input_interval": "[-1, 1]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-1, 1] has a real-rooted image" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 6ca2387dc1877086fd210c2f2736e0c35397c9036f75a7aa35254cf773155148, 3,423 bytes (1,219 compressed); download JSON

Cited by

• n-4ca7e225b5e9bcc6 (basis_map_preserver)