Proof step e-febd753f2a0fea62

basis_map_theorem → concludes about Pascal-(1,4,1) 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": "[-4 - sqrt(20), -4 + sqrt(20)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-4 - sqrt(20), -4 + sqrt(20)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-4 - sqrt(20), -4 + sqrt(20)]", "output_interval": "[-9 - 2 sqrt(20), -9 + 2 sqrt(20)]", "statement": "every real polynomial with all roots in E = [-4 - sqrt(20), -4 + sqrt(20)] has an image with all roots in I = [-9 - 2 sqrt(20), -9 + 2 sqrt(20)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-4 - sqrt(20), 0]", "output_interval": "[-9 - 2 sqrt(20), -9 + 2 sqrt(20)]", "statement": "every PF input with all roots in [-4 - sqrt(20), 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 3f9c493811ae7e1bc9a1599dfdce679e2b412817c05978e024909f42b7eaa285, 5,808 bytes (1,465 compressed); download JSON

Cited by

• n-ed9434bfd889c409 (basis_map_preserver)