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Proof step 27 from proof hasSharing-put-statfield (previous step)

(st[jvmref -- sk, val][jvmref -- sks]) = refval(r0), (st[jvmref -- sk, val][jvmref -- (sk0 ' + sks1)]) = refval(r0), fits(jvmref, sks, st), fits(jvmref, sk0 ' + sks1, st), ∀ st, sk, val, sks, r0. (st[jvmref -- sk, val][jvmref -- sks]) = refval(r0) ∧ (st[jvmref -- sk, val][jvmref -- sks1]) = refval(r0) ∧ fits(jvmref, sks1, st) ∧ fits(jvmref, sks, st) ∧ (st[jvmref -- sks] .refval = jvmref ∨ st[jvmref -- sks] ≠ st[jvmref -- sks1]) → sks1 = sks ∨ sks1 = [] ∨ sks = [] ∨ r0 = jvmref, st[jvmref -- sks] .refval = jvmref ∨ st[jvmref -- sks] ≠ st[jvmref -- (sk0 ' + sks1)] ⊦ sks = [], r0 = jvmref, sk0 ' + sks1 = sks

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ fits(r, sk ' + sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval) ∧ fits(st[r -- sk] .refval, sks, st)

Rule argument

[crewrite-arg: fits-storekeys-rec , F , [st, sks, sk, r] → [st, sks1, sk0, jvmref] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, sks1, sk0, jvmref)]]