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Proof step 16 from proof ac-dups-02 (previous step)

sk0 = fs ', is_fskey(sk0), ∀ class1, sk, val, val0, fis1, st. addclass(class1, fis0 + (sk × val) ' + (sk × val0) ' + fis1, st) = addclass(class1, fis0 + (sk × val) ' + fis1, st) ⊦ addclass(class1, ((sk0 × val1) ' + fis0) + (sk × val) ' + (sk × val0) ' + fis1, st) = addclass(class1, ((sk0 × val1) ' + fis0) + (sk × val) ' + fis1, st), ¬ is_indexkey(sk0) ∧ fs .class ≠ class1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
∀ class1, sk, val, val0, fis1, st. addclass(class1, fis0 + (sk × val) ' + (sk × val0) ' + fis1, st) = addclass(class1, fis0 + (sk × val) ' + fis1, st) ⊦ addclass(fs .class, ((fs ' × val1) ' + fis0) + (sk × val) ' + (sk × val0) ' + fis1, st) = addclass(fs .class, ((fs ' × val1) ' + fis0) + (sk × val) ' + fis1, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(fs ')], [CSIMPSEQ : ⊦ is_fskey(fs ')])]]