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

validrefs(str, r ' + refs0, (st[jvmref -- sk, val][r -- _type]) .type, st), r ≠ jvmref ∨ _type ≠ sk ⊦ cyclic(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 10:
r -- _type ≠ jvmref -- sk, validrefs(str, r ' + refs0, st[r -- _type] .type, st), r ≠ jvmref ∨ _type ≠ sk ⊦ cyclic(str, r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- _type, val, jvmref -- sk, st] ,F ,store ,javastore ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (r -- _type, val, jvmref -- sk, st)]]