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Proof step 10 from proof add-nput-01 (previous step)

⊦ addobj(r, class1, fis + (sk × val) ' + fis0, st) = (addobj(r, class1, fis + fis0, st)[r -- sk, val]), sk ∈ fis

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ addobj(r, class1, (sk × val) ' + fis, st) = (addobj(r, class1, fis, st)[r -- sk, val])
Proof step 9:
∀ r, class1, sk, val, fis0, st. addobj(r, class1, fis1 + (sk × val) ' + fis0, st) = (addobj(r, class1, fis1 + fis0, st)[r -- sk, val]) ∨ sk ∈ fis1 ⊦ addobj(r, class1, (fv + fis1) + (sk × val) ' + fis0, st) = (addobj(r, class1, (fv + fis1) + fis0, st)[r -- sk, val]), sk ∈ fv + fis1

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ [] + fis = fis], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]