Proof step e-8caea9461a47d8d9

basis_map_theorem → concludes about Pascal-(1,3,1) array. 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": "[-3 - sqrt(12), -3 + sqrt(12)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-3 - sqrt(12), -3 + sqrt(12)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-3 - sqrt(12), -3 + sqrt(12)]", "output_interval": "[-7 - 2 sqrt(12), -7 + 2 sqrt(12)]", "statement": "every real polynomial with all roots in E = [-3 - sqrt(12), -3 + sqrt(12)] has an image with all roots in I = [-7 - 2 sqrt(12), -7 + 2 sqrt(12)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-3 - sqrt(12), 0]", "output_interval": "[-7 - 2 sqrt(12), -7 + 2 sqrt(12)]", "statement": "every PF input with all roots in [-3 - sqrt(12), 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 fdd72ea525e61356a6e2f467357af22da761f1a804a53e4b563539e85d41c2b6, 5,796 bytes (1,467 compressed); download JSON

Cited by

• n-d8f9ad9ce0e039d0 (basis_map_preserver)