Proof step e-9fb991ecf107efde

basis_map_theorem → concludes about Triangle of coefficients of Chebyshev's U(n,2*x-1) 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": "[0, 1]", "statement": "every real polynomial with all roots in E = [-1, 1] has an image with all roots in I = [0, 1]" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 7a7556b2bb984e03741a7288aa36af328e19979dcb97f49d0573f000db83cd91, 4,285 bytes (1,275 compressed); download JSON

Cited by

• n-3a7609bd7546c802 (basis_map_preserver)