Proof step e-439c4d4974bd964a

basis_map_theorem → concludes about Pascal-(1,9,1) array. 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": "[-9 - sqrt(90), -9 + sqrt(90)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-9 - sqrt(90), -9 + sqrt(90)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-9 - sqrt(90), -9 + sqrt(90)]", "output_interval": "[-19 - 2 sqrt(90), -19 + 2 sqrt(90)]", "statement": "every real polynomial with all roots in E = [-9 - sqrt(90), -9 + sqrt(90)] has an image with all roots in I = [-19 - 2 sqrt(90), -19 + 2 sqrt(90)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-9 - sqrt(90), 0]", "output_interval": "[-19 - 2 sqrt(90), -19 + 2 sqrt(90)]", "statement": "every PF input with all roots in [-9 - sqrt(90), 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 616b98beca0296fd41466e5df2890a68c6c930c888cbf1ae383e2ffc479c9c04, 5,817 bytes (1,469 compressed); download JSON

Cited by

• n-7ac21ea1b3b7e282 (basis_map_preserver)