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Proof step 10 from proof update-put-same (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, [], st) = st
Proof step 9:
∀ sk, r, st, val. sk ∈ fis0 → update(r, fis0, st[r -- sk, val]) = update(r, fis0, st), sk ∈ fv + fis0 ⊦ update(r, fv + fis0, st[r -- sk, val]) = update(r, fv + fis0, st)

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPSEQ : ⊦ ¬ sk ∈ []])]]