Proof step e-4036622c95205ccf

basis_map_theorem → concludes about Triangular array formed by the Mersenne numbers. 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": "[-sqrt(2), sqrt(2)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-sqrt(2), sqrt(2)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-sqrt(2), sqrt(2)]", "output_interval": "[-3 - 2 sqrt(2), -3 + 2 sqrt(2)]", "statement": "every real polynomial with all roots in E = [-sqrt(2), sqrt(2)] has an image with all roots in I = [-3 - 2 sqrt(2), -3 + 2 sqrt(2)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-sqrt(2), 0]", "output_interval": "[-3 - 2 sqrt(2), -3 + 2 sqrt(2)]", "statement": "every PF input with all roots in [-sqrt(2), 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 13b91352fa48e3929b531db58d4a916d99d0a2a0c37cf9f17fb7bbf3f6969bb8, 5,729 bytes (1,457 compressed); download JSON

Cited by

• n-9b5c7e97e5191da6 (basis_map_preserver)