Proof step `e-08a1e090b4e4ea0b`

basis_map_theorem → concludes about Riordan array (1-x,x/(1-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, 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" }

polytool: replayed (the certificate replayed when the step was written)
Lean: not attempted
certificate: basis_map_theorem, SHA-256 58100c40a70d68ab8bdbd6de2a913033d4e36d699ef5a838fa239498c82653f8, 1,858 bytes (717 compressed); download JSON