Proof step e-013b61d0172203f3

basis_map_theorem → concludes about Triangle of coefficients of Chebyshev's S(n,x+4) 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": "[-6, -2]", "statement": "every real polynomial with all roots in E = [-1, 1] has an image with all roots in I = [-6, -2]" }
• { "claim": "basis_map_preserver", "input_interval": "[-1, 0]", "output_interval": "[-6, -2]", "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 f7436e3b494fe470318684a0445dc5275ff32c7ff96621167cc2366618ecad60, 5,299 bytes (1,355 compressed); download JSON

Cited by

• n-30cb3cad216ed189 (basis_map_preserver)