Manuscript XXII-D@1 · XXII-D.tex · corollary · 17889d18

Corollary: Design and implementation allowances

Complete-channel transport and error assembly › Telescoping on actual compatible interfaces · lines 873–895 · proof included or linked

XXII-D@1#cor:assembly, XXII-D@1#eq:assembled

If also

d_{⋄} (Γ_{n}, Θ_{n}) \leq μ_{n},

then

d_{⋄} (Γ_{n}, Θ_{n}) \leq min {1, μ_{n} + α_{n} + j = 1 \sum^{k_{n}} e_{n, j} + β_{n}} .

If $k_{n} \leq H_{n}$ and $e_{n, j} \leq ϵ_{n}$ , the sum is at most $H_{n} ϵ_{n}$ .

Proof. Apply Lemma lem:telescoping, then the triangle inequality with $Θ_{n}$ , and cap the result at one.

Displayed formulas in this passage

unlabeled · line 876
$d_{⋄} (Γ_{n}, Θ_{n}) \leq μ_{n},$
XXII-D@1#eq:assembled · line 880
$d_{⋄} (Γ_{n}, Θ_{n}) \leq min {1, μ_{n} + α_{n} + j = 1 \sum^{k_{n}} e_{n, j} + β_{n}} .$