Proof step e-d4a7bd772f22ef34

basis_map_theorem → concludes about a(n) = 1 if n is of the form m(m+3)/2, otherwise 0. JSON

Theorem

Geometric basis map (elementary) polytool ?

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": "(-inf, +inf)", "output_interval": "(-inf, +inf)", "statement": "every real-rooted input has a real-rooted image (an affine substitution times g)" }
• { "claim": "basis_map_preserver", "input_interval": "(-inf, 0]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 0 gives the root (r - a)/d <= 0; a larger root gives a positive root" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 18d4ed472ce4f1e761fc4708332bdcfd56a87ea225a01b47adc2cdad870fc2df, 1,865 bytes (717 compressed); download JSON

Cited by

• n-6fea5aff4f44fa54 (basis_map_preserver)