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Proof step 13 from proof put-put-switch (previous step)

⊦ sks0 = [], (st[r -- sk, val][r0 -- sks0, val0]) = (st[r0 -- sks0, val0][r -- sk, val]), sk ∈ sks0

User applied rule structural induction

And obtained the following new goals

Proof step 12:
∀ st, r, sk, val, r0, val0. sks = [] ∨ (st[r -- sk, val][r0 -- sks, val0]) = (st[r0 -- sks, val0][r -- sk, val]) ∨ sk ∈ sks ⊦ sk0 + sks = [], (st[r -- sk, val][r0 -- (sk0 + sks), val0]) = (st[r0 -- (sk0 + sks), val0][r -- sk, val]), sk ∈ sk0 + sks

Rule argument

[VARWITHVARSEQSARG : sks0, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : storekeys generated by [], +;])]]