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Proof step 26 from proof ac-dups-02 (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ is_fskey(fv .1) ∧ fv .1 .fs .class ≠ class → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 18:
¬ (is_fskey((sk0 × val1) .1) ∧ (sk0 × val1) .1 .fs .class ≠ class1), 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)
Proof step 25:
is_fskey((sk0 × val1) .1) ∧ (sk0 × val1) .1 .fs .class ≠ class1, 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, fis0 + (sk × val) ' + (sk × val0) ' + fis1, st) = addclass(class1, ((sk0 × val1) ' + fis0) + (sk × val) ' + fis1, st)

Rule argument

[crewrite-arg: ac-no1 , F , [st, fis, fv, class] → [st, fis0 + (sk × val) ' + (sk × val0) ' + fis1, sk0 × val1, class1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])], [EXTRATERMS : (st, fis0 + (sk × val) ' + (sk × val0) ' + fis1, sk0 × val1, class1)]]