Proof step e-764dc90b5c153977

basis_map_theorem → concludes about Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2… 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, 0]", "output_interval": "(-inf, 0]", "statement": "an input root r <= 0 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 84dc21b1f5ef5ab4bdfba02c71ec873d26ac70258d2745b9e178c1d26217812f, 1,991 bytes (785 compressed); download JSON

Cited by

• n-ae7910bbe46f8a41 (basis_map_preserver)