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Proof step 9 from proof update-atin (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, [], st) = st
Proof step 8:
∀ sk, r, st. sk ∈ fis0 → (update(r, fis0, st)[r -- sk]) = fis0[sk], sk ∈ fv + fis0 ⊦ (update(r, fv + fis0, st)[r -- sk]) = (fv + fis0)[sk]

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

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