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Proof step 9 from proof update-union-switch (previous step)

∀ r, st, st0. update(r, fis0, st ∪ st0) = st ∪ update(r, fis0, st0) ∨ r ∈ st .refs ⊦ (update(r, fis0, st ∪ st0)[r -- fv .1, fv .2]) = st ∪ (update(r, fis0, st0)[r -- fv .1, fv .2]), r ∈ st .refs

User applied rule structural induction

And obtained the following new goals

Proof step 8:
∀ r, st, st0. update(r, fis0, st ∪ st0) = st ∪ update(r, fis0, st0) ∨ r ∈ st .refs ⊦ (update(r, fis0, st ∪ st0)[r -- (sk × val) .1, (sk × val) .2]) = st ∪ (update(r, fis0, st0)[r -- (sk × val) .1, (sk × val) .2]), r ∈ st .refs

Rule argument

[VARWITHVARSEQSARG : fv, ()]

Additional information

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