R0039-20406 · q-20261014-advance-20261107-r07-subsequence-0031
自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={"source_start":6,"source_step":6,"index_start":1,"index_step":1,"j":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — 自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={"source_start":6,"source_step":6,"index_start":1,"index_step":1,"j":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。
操作前
source operation=subseq-arithmetic-term;original snapshot and mathematics retained
操作後
explicit ordered source output fields=[j, source_index, subsequence_term, certificate]
條件：無
原題快照保留歷史介面標記；本頁直接列來源欄位順序，不需JavaScript或外部表。欄位標籤不是額外數學證據，No保持原題的聲稱範圍。
規則：source_ordered_interface_explicit_without_javascript · 依賴：G001
操作前
original subsequence index k:ORIGINAL nonnegative start=1;positive integer step=1;F(q)=start+step*q for EVERY natural q>=0
操作後
F(q)>=start>=0 and for ANY q<r,F(r)-F(q)=(1)*(r-q)>0;strictly increasing on ALL naturals,not just the evaluated prefix
條件：無
正整數step讓任意兩個自然索引的差都保持正，故保原順序，不只是單射或任意重排。此全稱數學law不以某個數值輸出安全範圍截斷，也不宣稱原數列的值遞增。
規則：subseq_affine_all_natural_index_order_not_value_monotonicity · 依賴：G001, S001
操作前
subsequence selected index step times j := mul(1, 7)
操作後
subsequence selected index step times j = 7
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S002
操作前
subsequence selected ORIGINAL source index := sum(1, 7)
操作後
subsequence selected ORIGINAL source index = 8
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S003
操作前
subsequence ORIGINAL source step times selected index := mul(6, 8)
操作後
subsequence ORIGINAL source step times selected index = 48
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S004
操作前
subsequence value of ORIGINAL source at selected index := sum(6, 48)
操作後
subsequence value of ORIGINAL source at selected index = 54
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S005
操作前
ORIGINAL arithmetic source a_n=6+(6)n;increasing selected index k(7)=8
操作後
a_at_selected_index=54;ORIGINAL index order retained even if source step=6 is negative or0;no value sorting
條件：無
先核索引，再代回原source公式；sourceStep可負或0，子序列保留原索引次序而非要求值向上。不得把數值排序後的集合另叫本題子序列。
規則：subseq_selected_source_order_not_reordered_values · 依賴：G001, S006
S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S006 · premise_and_result_audit — 以精確有理數重算 subsequence value of ORIGINAL source at selected index，不以小數近似替代。S005 · premise_and_result_audit — 以精確有理數重算 subsequence ORIGINAL source step times selected index，不以小數近似替代。S004 · premise_and_result_audit — 以精確有理數重算 subsequence selected ORIGINAL source index，不以小數近似替代。S003 · premise_and_result_audit — 以精確有理數重算 subsequence selected index step times j，不以小數近似替代。S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。(7, 8, 54, a_of_k_j_preserves_original_order)
依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。
覆核日期：2026-10-26
原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: bba4e2cee0e85e628359e1678ea877c1c9114df6315926842fb673e6082345d4candidate record SHA-256: 880d7006764aada687bd03022b3e79cf8f902cb2fb01b708b25f62fdbe36490dsemantic review receipt SHA-256: 6e11e35fafe32f16900ce9b522d01acb7b2ee6b463ab179392076cfbe1af8034question-first witness SHA-256: cc0fa361fc25151729e70264340d2eae94f179f6f2a2edfe80ba5704fbbd0682Lean: NOT_RUN · human review: NOT_PERFORMED