Proof step e-a8d04e97d37c94ea

basis_map_theorem → concludes about Pascal-(1,8,1) 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": "[-8 - sqrt(72), -8 + sqrt(72)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-8 - sqrt(72), -8 + sqrt(72)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-8 - sqrt(72), -8 + sqrt(72)]", "output_interval": "[-17 - 2 sqrt(72), -17 + 2 sqrt(72)]", "statement": "every real polynomial with all roots in E = [-8 - sqrt(72), -8 + sqrt(72)] has an image with all roots in I = [-17 - 2 sqrt(72), -17 + 2 sqrt(72)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-8 - sqrt(72), 0]", "output_interval": "[-17 - 2 sqrt(72), -17 + 2 sqrt(72)]", "statement": "every PF input with all roots in [-8 - sqrt(72), 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 86ddcff140ef3f1fa5d4932e717c63aa94ac1770438f73d0a653c1098a933b9a, 5,799 bytes (1,469 compressed); download JSON

Cited by

• n-1c472d1762258215 (basis_map_preserver)