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Proof step 11 from proof validfieldlist-put-statfield (previous step)

r ≠ jvmref ∨ ¬ sk ∈ sks ⊦ validfieldlist(str, r, sks, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sks, st)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ validfieldlist(str, r, [], st)
Proof step 10:
∀ r, sk, str, st, val. r ≠ jvmref ∨ ¬ sk ∈ sks0 → (validfieldlist(str, r, sks0, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sks0, st)), r ≠ jvmref ∨ ¬ sk ∈ sk0 + sks0 ⊦ validfieldlist(str, r, sk0 + sks0, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sk0 + sks0, st)

Rule argument

[VARWITHVARSEQSARG : sks, ()]

Additional information

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