Proof step `e-468701cdcc848e53`

basis_map_theorem → concludes about Riordan array ((1+x)^3,x). JSON

Theorem

Geometric basis map (elementary) polytool ?

Basis map theorem for the node's own rule

{
  "operation": "basis_map_theorem"
}

None: this step is a direct theorem check.

{ "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, 0]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 0 gives the root (r - a)/d <= 0; a larger root gives a positive root" }

polytool: replayed (the certificate replayed when the step was written)
Lean: not attempted
certificate: basis_map_theorem, SHA-256 1149ca7f69460456aabccfa46290ea5106f3afbf6693793e6881df63a5b7a848, 1,864 bytes (709 compressed); download JSON