Proof step e-d8c18795222de68a

basis_map_theorem → concludes about Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is a pair of identical consecutive le… 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, 2]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 2 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 0f800e1d5cfd95db6becd3ce5a061d16cb62ec6cfb921ce6078723f9e98e27a4, 1,979 bytes (802 compressed); download JSON

Cited by

• n-51b4f5e7901c2b50 (basis_map_preserver)