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Proof step 11 from proof add-nput-02 (previous step)

⊦ addobj(r, class1, fis + (sk × val) ', st) = (addobj(r, class1, fis, 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) ', st) = (addobj(r, class1, [], st)[r -- sk, val])
Proof step 2:
⊦ addobj(r, class1, [], st) = st[r -- _type, typeval(mkclasstype(class1))]
Proof step 10:
∀ r, class1, sk, val, st. addobj(r, class1, fis0 + (sk × val) ', st) = (addobj(r, class1, fis0, st)[r -- sk, val]) ∨ sk ∈ fis0 ⊦ addobj(r, class1, (fv + fis0) + (sk × val) ', st) = (addobj(r, class1, fv + fis0, st)[r -- sk, val]), sk ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

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