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Question 8663: Explicit Incidence

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0016-08663 · q-20260917-explicit-incidence-language-0013

Original question and givens

Explicit incidence data: P13 lies on l13. Is P13 incident with l13?

  • G001 — Explicit incidence data: P13 lies on l13. Is P13 incident with l13?

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

explicit typed incidence data;no coordinate or visual premise supplied

After

read the stated predicate;absence of a premise is not its negation

Conditions: none

Read the explicit geometric premise without inferring from appearance.An absent premise is not a negative premise;do not invent coordinates or equations.

Step identifiers and dependencies

Rule: declared_geometry_not_visual_inference · Uses: G001

S002 · implies

Before

point=P13;line=l13;declared on=Yes

After

incident=Yes

Conditions: none

Here a point is incident with the line exactly when it lies on it.An explicit not-on premise gives nonincidence;retain the original labels.

Step identifiers and dependencies

Rule: incidence_definition_from_explicit_premise · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

Yes

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: accfbad9e1beccf743b43349af761fb528851b36145b72bc8899978f75491e65
  • candidate record SHA-256: 669df5a74433a3e72007a263e0b3d3059c0fb1a490df5b115216e30a3bcdd5c7
  • semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2
  • question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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