Proof step e-0f2818456c73ddce

basis_map_theorem → concludes about Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). 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, 1]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 1 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 c2bc44c02e0dbaa31df353db969bf3200b10b824841cef004b1de39f12cd8598, 1,865 bytes (739 compressed); download JSON

Cited by

• n-089a9b4f824a1c20 (basis_map_preserver)