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Proof step 7 from proof update-atin (previous step)

sk ∈ fv ' + fis0, ∀ sk, r, st. sk ∈ fis0 → (update(r, fis0, st)[r -- sk]) = fis0[sk] ⊦ (update(r, fv ' + fis0, st)[r -- sk]) = (fv ' + fis0)[sk]

User applied rule structural induction

And obtained the following new goals

Proof step 6:
sk ∈ (sk0 × val) ' + fis0, ∀ sk, r, st. sk ∈ fis0 → (update(r, fis0, st)[r -- sk]) = fis0[sk] ⊦ (update(r, (sk0 × val) ' + fis0, st)[r -- sk]) = ((sk0 × val) ' + fis0)[sk]

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldvalue generated by ×;])]]