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Proof step 4 from proof update-union-switch (previous step)

∀ r, st, st0. update(r, fis0, st ∪ st0) = st ∪ update(r, fis0, st0) ∨ r ∈ st .refs ⊦ (st ∪ update(r, fis0, st0))[r -- sk, val] = st ∪ (update(r, fis0, st0)[r -- sk, val]), r ∈ st .refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ st ∪ st0[rk, val] = (st ∪ st0)[rk, val]

Rule argument

[speclemmaarg: ,st ∪ st0[rk, val] = (st ∪ st0)[rk, val] ,[val, rk, st0, st] → [val, r -- sk, update(r, fis0, st0), st] ,F ,storefunsx , ,union-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, r -- sk, update(r, fis0, st0), st)]]