Proof step e-c9d1880c7ed7baa2

basis_map_theorem → concludes about Riordan array (1/(1-2*x), x*(1+x)/(1-2*x)). 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 - sqrt(3), -1 + sqrt(3)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-1 - sqrt(3), -1 + sqrt(3)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-1 - sqrt(3), -1 + sqrt(3)]", "output_interval": "[-4 - 2 sqrt(3), -4 + 2 sqrt(3)]", "statement": "every real polynomial with all roots in E = [-1 - sqrt(3), -1 + sqrt(3)] has an image with all roots in I = [-4 - 2 sqrt(3), -4 + 2 sqrt(3)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-1 - sqrt(3), 0]", "output_interval": "[-4 - 2 sqrt(3), -4 + 2 sqrt(3)]", "statement": "every PF input with all roots in [-1 - sqrt(3), 0] has a PF image; no larger [-R, 0] works" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 97c3275b8411f9533d03c3f30d8285560735e571774b3d24032b015595ba86a6, 5,800 bytes (1,474 compressed); download JSON

Cited by

• n-d5c14b9fec875ecc (basis_map_preserver)