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Proof step 8 from proof hasKeys-put (previous step)

⊦ r = r0, hasKeys(r, sks, st[r0 -- sk, val]) ↔ hasKeys(r, sks, st)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ hasKeys(r, [], st)
Proof step 7:
∀ r, r0, st, sk, val. r = r0 ∨ (hasKeys(r, sks0, st[r0 -- sk, val]) ↔ hasKeys(r, sks0, st)) ⊦ r = r0, hasKeys(r, sk0 + sks0, st[r0 -- sk, val]) ↔ hasKeys(r, sk0 + sks0, st)

Rule argument

[VARWITHVARSEQSARG : sks, ()]

Additional information

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