Proof step e-bfd6a840c4d6eb68

basis_map_theorem → concludes about Pascal-(1,2,1) array read by antidiagonals. 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": "[-2 - sqrt(6), -2 + sqrt(6)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-2 - sqrt(6), -2 + sqrt(6)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-2 - sqrt(6), -2 + sqrt(6)]", "output_interval": "[-5 - 2 sqrt(6), -5 + 2 sqrt(6)]", "statement": "every real polynomial with all roots in E = [-2 - sqrt(6), -2 + sqrt(6)] has an image with all roots in I = [-5 - 2 sqrt(6), -5 + 2 sqrt(6)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-2 - sqrt(6), 0]", "output_interval": "[-5 - 2 sqrt(6), -5 + 2 sqrt(6)]", "statement": "every PF input with all roots in [-2 - sqrt(6), 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 371f7211e80202efb3797524e0aa44761065bc5fa9b2bbd3e8e50da1239b0e2a, 5,798 bytes (1,472 compressed); download JSON

Cited by

• n-f25cd955a876cde3 (basis_map_preserver)