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Proof step 7 from proof update-at-notin (previous step)

⊦ (update(r, fis, st)[r0 -- sk]) = st[r0 -- sk], sk ∈ fis

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, [], st) = st
Proof step 6:
∀ r, st, r0, sk. (update(r, fis0, st)[r0 -- sk]) = st[r0 -- sk] ∨ sk ∈ fis0 ⊦ (update(r, fv + fis0, st)[r0 -- sk]) = st[r0 -- sk], sk ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

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