Proof step e-6f75aea89a6e01af

basis_map_theorem → concludes about Triangle of coefficients in expansion of (2+3x)^n. 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 4d5afddc0bf8bc6c59decb68c95ace54bc1ea439aa5c3c52ceebe13af8ee2116, 1,864 bytes (727 compressed); download JSON

Cited by

• n-5733d79f45a14084 (basis_map_preserver)