Proof step e-05b27694ad6bb7e9

basis_map_theorem → concludes about a(n) = 1 if n is a triangular number, 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, 1]", "output_interval": "(-inf, 0]", "statement": "T(p) = p(a) g; an input with every root <= a has p(a) of the sign of its leading coefficient" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 13a78b7404877090184ee9df3ef1f6501f03fdcecec033d304812d0027b41555, 1,619 bytes (671 compressed); download JSON

Cited by

• n-39194b37db596ae8 (basis_map_preserver)