Proof step e-39fc4711b1b8289f

basis_map_theorem → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*6^j. 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, 8]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 8 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 f1faf92361d71951aadd468849d4bbe0bd78a182db8a8a94b40325c8e081f1b5, 1,895 bytes (751 compressed); download JSON

Cited by

• n-c11cb6bca0e3e7dc (basis_map_preserver)