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Proof step 9 from proof ac-bad-02 (previous step)

is_fskey(sk), ∀ class1, i, val, fis1, st. addclass(class1, fis0 + (i ' × val) ' + fis1, st) = addclass(class1, fis0 + fis1, st) ⊦ addclass(class1, ((sk × val0) ' + fis0) + (i ' × val) ' + fis1, st) = addclass(class1, ((sk × val0) ' + fis0) + fis1, st), ¬ is_indexkey(sk) ∧ sk .fs .class ≠ class1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
sk = fs ', is_fskey(sk), ∀ class1, i, val, fis1, st. addclass(class1, fis0 + (i ' × val) ' + fis1, st) = addclass(class1, fis0 + fis1, st) ⊦ addclass(class1, ((sk × val0) ' + fis0) + (i ' × val) ' + fis1, st) = addclass(class1, ((sk × val0) ' + fis0) + fis1, st), ¬ is_indexkey(sk) ∧ fs .class ≠ class1

Rule argument

[speclemmaarg: ,is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') ,[sk, fs] → [sk, fs] ,T ,storekey , ,elim-03 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]