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Proof step 5 from proof update-at-notin (previous step)

∀ r, st, r0, sk. (update(r, fis0, st)[r0 -- sk]) = st[r0 -- sk] ∨ sk ∈ fis0 ⊦ (update(r, fis0, st)[r -- fv .1, fv .2][r0 -- sk]) = st[r0 -- sk], sk ∈ fv ', sk ∈ fis0

User applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ r, st, r0, sk. (update(r, fis0, st)[r0 -- sk]) = st[r0 -- sk] ∨ sk ∈ fis0 ⊦ (update(r, fis0, st)[r -- (sk0 × val) .1, (sk0 × val) .2][r0 -- sk]) = st[r0 -- sk], sk ∈ (sk0 × val) ', sk ∈ fis0

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

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