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

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

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