Proof step `e-e353876edd912a5b`

basis_map_theorem → concludes about Pascal-(1,5,1) array. JSON

Theorem

Basis map theorem for the node's own rule

{
  "operation": "basis_map_theorem"
}

None: this step is a direct theorem check.

{ "claim": "basis_map_preserver", "input_interval": "[-5 - sqrt(30), -5 + sqrt(30)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-5 - sqrt(30), -5 + sqrt(30)] has a real-rooted image" }
{ "claim": "basis_map_preserver", "input_interval": "[-5 - sqrt(30), -5 + sqrt(30)]", "output_interval": "[-11 - 2 sqrt(30), -11 + 2 sqrt(30)]", "statement": "every real polynomial with all roots in E = [-5 - sqrt(30), -5 + sqrt(30)] has an image with all roots in I = [-11 - 2 sqrt(30), -11 + 2 sqrt(30)]" }
{ "claim": "basis_map_preserver", "input_interval": "[-5 - sqrt(30), 0]", "output_interval": "[-11 - 2 sqrt(30), -11 + 2 sqrt(30)]", "statement": "every PF input with all roots in [-5 - sqrt(30), 0] has a PF image; no larger [-R, 0] works" }

polytool: replayed (the certificate replayed when the step was written)
Lean: not attempted
certificate: basis_map_theorem, SHA-256 297387bf0f38a755608c5343720d1c98fe2681062f6ee3857f5e1ab84a0fd182, 5,817 bytes (1,461 compressed); download JSON