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R0070-35959 · q-20261003-advance-20261004-r05-vector-0084
In the fixed basis of the real plane R², u=(-4, 1) and v=(-4, 1). Are u and v equal?
G001 — In the fixed basis of the real plane R², u=(-4, 1) and v=(-4, 1). Are u and v equal?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.
Before
source roles = [qf-vector-coordinate-equality, [domain, operation, u, v]]
After
derived = [vector, vector_equality, reals]
Conditions: none
Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.
Rule: R70_SOURCE_bank_specific_interface · Uses: G001
Before
source roles = [[-4, 1], [-4, 1], null]
After
derived = [two real coordinates in ONE ordered basis]
Conditions: none
The vectors use ONE ordered basis.Type ALL TWO RAW SAFE components and k.These are vector coordinates,not points,lengths or a dot product.Component sums alone do not determine equality.
Rule: Vector_GIVEN_common_ordered_basis_RAW_two_SAFE_components · Uses: G001, S001
Before
source roles = [0, -4, -4]
After
derived = [Yes]
Conditions: none
Compare EACH corresponding position without permuting coordinates.Vector equality requires BOTH components to match.
Rule: Vector_EQUALITY_EACH_corresponding_coordinate · Uses: G001, S002
Before
source roles = [1, 1, 1]
After
derived = [Yes]
Conditions: none
Compare EACH corresponding position without permuting coordinates.Vector equality requires BOTH components to match.
Rule: Vector_EQUALITY_EACH_corresponding_coordinate · Uses: G001, S003
Before
source roles = [[Yes, Yes]]
After
derived = [Yes]
Conditions: none
Conjoin BOTH coordinate equalities;neither one match nor equal component sums is enough.
Rule: Vector_EQUALITY_conjunction_not_component_sum · Uses: G001, S004
S005 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S004 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.Yes
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 759931bb86b618536eb90fb874bdc61b566f407a9359c6e45fb198acb4e38afdcandidate record SHA-256: a30b71a8f1009266e648b5fc14395a748e67bd1ed121af10ec7ea9966841ecf1semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED