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Proof step 9 from proof subset-putarray2-addarray-newref (previous step)

newref(r, st) ⊦ r = jvmref, st ⊆ putArray(vals0, r, i, putArray(vals1, r, j, addarray(r, ty, vals, st)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 8:
newref(r, st) ⊦ r = jvmref, ∀ rk. rk ∈ st → rk ∈ putArray(vals0, r, i, putArray(vals1, r, j, addarray(r, ty, vals, st))) ∧ st[rk] = (putArray(vals0, r, i, putArray(vals1, r, j, addarray(r, ty, vals, st)))[rk])

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [putArray (vals0, r, i, putArray(vals1, r, j, addarray(r, ty, vals, st))), st] ,F ,store ,javastore ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (putArray (vals0, r, i, putArray(vals1, r, j, addarray(r, ty, vals, st))), st)]]