Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=8≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).
G001 — Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=8≥0 and positive integer index_step=4. Give (index_start, index_step, index_formula, strictly_increasing, certificate).
Definition and scope
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original subsequence index k:ORIGINAL nonnegative start=8;positive integer step=4;F(q)=start+step*q for EVERY natural q>=0
After
F(q)>=start>=0 and for ANY q<r,F(r)-F(q)=(4)*(r-q)>0;strictly increasing on ALL naturals,not just the evaluated prefix
Conditions: none
A positive integer step preserves the order of every pair of natural indices,not merely injectivity or an arbitrary reordering.This universal mathematical law is not truncated by an evaluated-output safety range and says nothing about monotonicity of source values.
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.