Proof step e-d4a7a90d58b7b7be

basis_map_theorem → concludes about Pascal-(1,6,1) 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": "[-6 - sqrt(42), -6 + sqrt(42)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-6 - sqrt(42), -6 + sqrt(42)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-6 - sqrt(42), -6 + sqrt(42)]", "output_interval": "[-13 - 2 sqrt(42), -13 + 2 sqrt(42)]", "statement": "every real polynomial with all roots in E = [-6 - sqrt(42), -6 + sqrt(42)] has an image with all roots in I = [-13 - 2 sqrt(42), -13 + 2 sqrt(42)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-6 - sqrt(42), 0]", "output_interval": "[-13 - 2 sqrt(42), -13 + 2 sqrt(42)]", "statement": "every PF input with all roots in [-6 - sqrt(42), 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 4a71f70a189a2eba016cdf8a8ae55f48bc7f24abcefa79e42b68c413076dd580, 5,817 bytes (1,469 compressed); download JSON

Cited by

• n-212fa067c32397af (basis_map_preserver)