Proof step e-71cb1ba62d8762b5

basis_map_theorem → concludes about Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j. 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, 3]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 3 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 c90c49f1f8d4e660952f2a5061394e446e4f29145e2f48c4e296966582fdf14b, 1,901 bytes (756 compressed); download JSON

Cited by

• n-26633b980c3508e8 (basis_map_preserver)