Proof step e-f2166ff27dacf1fa

basis_map_theorem → concludes about Triangle of coefficients of polynomials v(n,x) jointly generated with A207606; see Formula section. 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": "[-4, 0]", "statement": "every real polynomial with all roots in E = [-1, 1] has an image with all roots in I = [-4, 0]" }
• { "claim": "basis_map_preserver", "input_interval": "[-1, 0]", "output_interval": "[-4, 0]", "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 a4a7b8e8ed9819fbf59708eee9e62663de2db5b57e4f74ec3aedb76c20b57d25, 5,290 bytes (1,366 compressed); download JSON

Cited by

• n-353fb5a029e4e669 (basis_map_preserver)