Proof step e-885864d02a352890

basis_map_theorem → concludes about Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments. 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 d8a630148e7f374ef04cf0d4bd192b2cca2fd88fc95643943989463f68d37890, 5,848 bytes (1,504 compressed); download JSON

Cited by

• n-eac80c2bf8e566f5 (basis_map_preserver)