fact: Definition DecomposeRawQueryStructureSchema_AbsR {m : nat} {qs_schema : RawQueryStructureSchema} (schemaIdx : Fin.t _) (attrIdx : Fin.t _) (a : Vector.t Type m) (a_proj_index : Vector.nth (AttrList (GetNRelSchemaHeading (qschemaSchemas qs_schema) schemaIdx)) attrIdx -> Fin.t m) (a_proj : forall (attr : Vector.nth _ attrIdx), a[@a_proj_index attr]) (a_inj : forall idx, Vector.nth a idx -> Vector.nth (AttrList (GetNRelSchemaHeading (qschemaSchemas qs_schema) schemaIdx)) attrIdx) (r_o : UnConstrQueryStructure qs_schema) (r_n : UnConstrQueryStructure qs_schema * UnConstrQueryStructure (DecomposeRawQueryStructureSchema qs_schema schemaIdx attrIdx a)) : Prop := (forall Ridx, Same_set _ (GetUnConstrRelation r_o Ridx) (GetUnConstrRelation (fst r_n) Ridx)) /\ (forall Ridx tup, In _ (GetUnConstrRelation (snd r_n) Ridx) tup -> In _ (GetUnConstrRelation (fst r_n) schemaIdx) {| elementIndex := elementIndex tup; indexedElement := Tuple_DecomposeRawQueryStructure_inj' _ _ a a_inj _ (indexedElement tup) |}) /\ (forall tup, In _ (GetUnConstrRelation (fst r_n) schemaIdx) tup -> In _ (GetUnConstrRelation (snd r_n) (a_proj_index (GetAttributeRaw (indexedElement tup) attrIdx))) {| elementIndex := elementIndex tup; indexedElement := Tuple_DecomposeRawQueryStructure_proj' _ _ a _ a_proj (indexedElement tup) |}) /\ (forall Ridx Ridx' tup tup' , In _ (GetUnConstrRelation (snd r_n) Ridx) tup -> In _ (GetUnConstrRelation (snd r_n) Ridx') tup' -> Ridx <> Ridx' -> elementIndex tup <> elementIndex tup') /\ (forall Ridx tup, In IndexedElement (GetUnConstrRelation (snd r_n) Ridx) tup -> a_proj_index (GetAttributeRaw (Tuple_DecomposeRawQueryStructure_inj' _ _ a a_inj _ (indexedElement tup)) attrIdx) = Ridx) /\ (forall Ridx, FiniteEnsemble (GetUnConstrRelation (snd r_n) Ridx)).
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Vectors.Vector Coq.Strings.Ascii Coq.Bool.Bool Coq.Lists.List Fiat.Common.SumType Fiat.Computation.ListComputations Fiat.QueryStructure.Automation.AutoDB Bedrock.Word Bedrock.Memory