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Proof step 11 from proof update-put-notin (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ update(r, [], st) = st
Proof step 10:
∀ r0, st, sk, val. (update(r0, fis0, st)[r0 -- sk, val]) = update(r0, fis0, st[r0 -- sk, val]) ∨ sk ∈ fis0 ⊦ (update(r0, fv + fis0, st)[r0 -- sk, val]) = update(r0, fv + fis0, st[r0 -- sk, val]), sk ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

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