Proof step e-5ee7c33973be4058

basis_map_theorem → concludes about Triangle T(n,k), read by rows given by [1,0,1,0,0,0,0,0,0,...] DELTA [0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. 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, 0]", "output_interval": "(-inf, 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 67e1ce5ec01171ee7eb953367930989d71217a353511fd4eb728c7aa595b221d, 4,144 bytes (1,310 compressed); download JSON

Cited by

• n-01fe968f3e05a927 (basis_map_preserver)