Proof step e-d30779985c323b83

preserver_image affine, shift 0 → concludes about shift_x_plus_one of hermite_he JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

• hermite_he (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": {} }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 2bab898e31f0baa214cfd4b62a757ac03ebfc5e3e0c705705ef4761a2ccf763f, 12,731 bytes (2,680 compressed); download JSON

Cited by

• n-6a60232912a72903 (real_rooted)
• n-6a60232912a72903 (interlacing)