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Proof step 8 from proof subset-putarray-addarray-newref (previous step)

newref(r, st), r0 -- sk ∈ st, r0 -- sk ∈ putArray(vals0, r, i, addarray(r, ty, vals, st)), r0 ∈ st, r0 ∈ putArray(vals0, r, i, addarray(r, ty, vals, st)) ⊦ st[r0 -- sk] = (putArray(vals0, r, i, addarray(r, ty, vals, st))[r0 -- sk]), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ r ≠ r0 → (putArray(vals, r, j, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 7:
⊦ newref(r, st) ∧ r0 ∈ st → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[speclemmaarg: ,r ≠ r0 → (putArray(vals, r, j, st)[r0 -- sk]) = st[r0 -- sk] ,[sk, r0, st, j, r, vals] → [sk, r0, addarray(r, ty, vals, st), i, r, vals0] ,F ,storearrays , ,putar-atref ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ st → ¬ newref(r, st)])], [EXTRATERMS : (sk, r0, addarray(r, ty, vals, st), i, r, vals0)]]