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Proof step 37 from proof ac-dups-03 (previous step)

∀ class1, sk, val, fis1, val0, fis2, st. addclass(class1, fis0 + (sk × val) ' + fis1 + (sk × val0) ' + fis2, st) = addclass(class1, fis0 + (sk × val) ' + fis1 + fis2, st) ⊦ addclass(class1, (fv ' + fis0) + (sk × val) ' + fis1 + (sk × val0) ' + fis2, st) = addclass(class1, (fv ' + fis0) + (sk × val) ' + fis1 + fis2, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 31:
¬ is_indexkey(fv .1), ∀ class1, sk, val, fis1, val0, fis2, st. addclass(class1, fis0 + (sk × val) ' + fis1 + (sk × val0) ' + fis2, st) = addclass(class1, fis0 + (sk × val) ' + fis1 + fis2, st) ⊦ addclass(class1, (fv ' + fis0) + (sk × val) ' + fis1 + (sk × val0) ' + fis2, st) = addclass(class1, (fv ' + fis0) + (sk × val) ' + fis1 + fis2, st)
Proof step 36:
is_indexkey(fv .1), ∀ class1, sk, val, fis1, val0, fis2, st. addclass(class1, fis0 + (sk × val) ' + fis1 + (sk × val0) ' + fis2, st) = addclass(class1, fis0 + (sk × val) ' + fis1 + fis2, st) ⊦ addclass(class1, fis0 + (sk × val) ' + fis1 + (sk × val0) ' + fis2, st) = addclass(class1, (fv ' + fis0) + (sk × val) ' + fis1 + fis2, st)

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0 + (sk × val) ' + fis1 + (sk × val0) ' + fis2, fv, class1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])], [EXTRATERMS : (st, fis0 + (sk × val) ' + fis1 + (sk × val0) ' + fis2, fv, class1)]]