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Proof step 8 from proof update-put-same (previous step)

sk ∈ fv ' + fis0, ∀ sk, r, st, val. sk ∈ fis0 → update(r, fis0, st[r -- sk, val]) = update(r, fis0, st) ⊦ (update(r, fis0, st[r -- sk, val])[r -- fv .1, fv .2]) = (update(r, fis0, st)[r -- fv .1, fv .2])

User applied rule structural induction

And obtained the following new goals

Proof step 7:
sk ∈ (sk0 × val0) ' + fis0, ∀ sk, r, st, val. sk ∈ fis0 → update(r, fis0, st[r -- sk, val]) = update(r, fis0, st) ⊦ (update(r, fis0, st[r -- sk, val])[r -- (sk0 × val0) .1, (sk0 × val0) .2]) = (update(r, fis0, st)[r -- (sk0 × val0) .1, (sk0 × val0) .2])

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

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