Proof step e-85cb7c7abd19f98e

basis_map_theorem → concludes about Triangle read by rows of coefficients of Chebyshev's U(n,x) polynomials (exponents 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": "[-1, 1]", "statement": "every real polynomial with all roots in E = [-1, 1] has an image with all roots in I = [-1, 1]" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 2f85d5aec1776b399fac69ff8b62435e92eaf37f45748bd17b7ad89ee835f4c0, 4,293 bytes (1,257 compressed); download JSON

Cited by

• n-a2d7d802498a9d22 (basis_map_preserver)