Proof step e-822f6e0d1df19a88

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros). 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

• Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros). (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": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 1ec9b561e94b9f9974cfc75a6356870cb14ac384e295c10289df16b1aae47199, 16,297 bytes (3,818 compressed); download JSON

Cited by

• n-6379632195c99c4b (real_rooted)