Proof step e-d5b8d319fcb3f7e8

basis_map_theorem → concludes about Triangle whose (n,k)-th entry is 15^(n-k)*binomial(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, 15]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 15 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 a1327949c7ac69978abdc1f2ef26ad429c0035c5921fb2b1b99a1bd0d50a0f62, 1,877 bytes (736 compressed); download JSON

Cited by

• n-ff0214c333bfdcca (basis_map_preserver)