Real-rooted atlas

Proof step

Product of real-rooted factors (elementary)

A fixed real-rooted factor times a proved family factor [1+1], exponent 1 n + 1

Concludes
Triangle read by rows: T(n,k), for k=-n..n-1, is the scaled (by 2^n n!) probability that the sum of n uniform [-1, 1] variables is between k and k+1.
Premises
Theorem
polytool ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-4cd45aa0a6518701 · JSON
Operation
A fixed real-rooted factor times a proved family
{
  "exponent_offset": 1,
  "exponent_slope": 1,
  "factor": [
    "1",
    "1"
  ],
  "operation": "row_factor"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
row_factor, SHA-256 279dccca8959d2a20acbb32acbc853b8e7d96645690a1293a4eb18fb0b67c4ff, 4,811 bytes (1,444 compressed); download
polytool replayed the certificate when the step was written.
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