Proof step e-255cb8447a923811

basis_map_theorem → concludes about Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order). 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": "[-1, 1]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-1, 1] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-1, 1]", "output_interval": "[-7, -3]", "statement": "every real polynomial with all roots in E = [-1, 1] has an image with all roots in I = [-7, -3]" }
• { "claim": "basis_map_preserver", "input_interval": "[-1, 0]", "output_interval": "[-7, -3]", "statement": "every PF input with all roots in [-1, 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 e6fde85ebac5e5a68d7ec2bf629daca446b10bde21db78e34d9c15ea1f852f3c, 5,299 bytes (1,357 compressed); download JSON

Cited by

• n-c2b7c74f8491f01b (basis_map_preserver)