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Proof step 10 from proof update-keyin (previous step)

⊦ r0 -- sk ∈ update(r, fis, st) ↔ r0 -- sk ∈ st, sk ∈ fis

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, [], st) = st
Proof step 9:
∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ update(r, fv + fis0, st) ↔ r0 -- sk ∈ st, sk ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

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