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Proof step 35 from proof ac-dups-03 (previous step)

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, fis0 + (sk × val) ' + fis1 + fis2, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 34:
fv = sk0 × val1, is_indexkey(sk0), ∀ 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, fis0 + (sk × val) ' + fis1 + fis2, st)

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk0, val1] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk0, val1)]]