Proof step e-9171fe67a9bd7e5c

basis_map_theorem → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*1^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, 12]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 12 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 1b316d4bf0f674918041e123dc45fdb616a943ed0ceaff974a44697e8c94bd1f, 1,881 bytes (737 compressed); download JSON

Cited by

• n-81e6fb4f9f226d77 (basis_map_preserver)