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Proof step 12 from proof in-list-put (previous step)

⊦ sks = [], r -- sks ∈ st[r0 -- sk, val] ↔ r -- sks ∈ st, sk ∈ sks

User applied rule structural induction

And obtained the following new goals

Proof step 11:
∀ r, st, r0, sk, val. sks0 = [] ∨ (r -- sks0 ∈ st[r0 -- sk, val] ↔ r -- sks0 ∈ st) ∨ sk ∈ sks0 ⊦ sk0 + sks0 = [], r -- (sk0 + sks0) ∈ st[r0 -- sk, val] ↔ r -- (sk0 + sks0) ∈ st, sk ∈ sk0 + sks0

Rule argument

[VARWITHVARSEQSARG : sks, ()]

Additional information

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