Proof step e-72ff8ab34d4573c3

basis_map_theorem → concludes about Cube of lower triangular normalized binomial matrix. 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 e8f4974c976fd2727e47294a37f93fbe5a685406c17c750e7ecdd8f30e3e168a, 1,866 bytes (733 compressed); download JSON

Cited by

• n-8d887bfc40d036b9 (basis_map_preserver)