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Proof step 14 from proof update-keyin-01 (conclusion)

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

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ update(r, [], st) = st
Proof step 13:
∀ r, sk, r0, st. r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis0 ⊦ r -- sk ∈ update(r0, fv + fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

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