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Proof step 13 from proof hasSharing-array-forward (previous step)

st[r0 -- sks0] = refval(r1), st[r -- i '] = refval(r0), st[r0 -- sks] = refval(r1), 0 < st[r -- _length] .intval, 0 ≤ i, is_arraytype(st[r -- _type] .type), i < st[r -- _length] .intval, fits(r0, sks, st), fits(r0, sks0, st) ⊦ sks0 = sks, sks0 = [], sks = [], r1 = jvmref, r = jvmref, fits(r, i ' ' + sks0, st) ∧ fits(r, i ' ' + sks, st) ∧ st[r -- (i ' ' + sks0)] .refval ≠ jvmref ∧ st[r -- (i ' ' + sks0)] = st[r -- (i ' ' + sks)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks]
Proof step 12:
sks ≠ [], st[r0 -- sks0] = refval(r1), st[r -- i '] = refval(r0), st[r0 -- sks] = refval(r1), 0 < st[r -- _length] .intval, 0 ≤ i, is_arraytype(st[r -- _type] .type), i < st[r -- _length] .intval, fits(r0, sks, st), fits(r0, sks0, st) ⊦ sks0 = sks, sks0 = [], sks = [], r1 = jvmref, r = jvmref, fits(r, i ' ' + sks0, st) ∧ fits(r, i ' ' + sks, st) ∧ st[r -- (i ' ' + sks0)] .refval ≠ jvmref ∧ st[r -- (i ' ' + sks0)] = st[st[r -- i '] .refval -- sks]

Rule argument

[speclemmaarg: ,sks ≠ [] → st[r -- (sk ' + sks)] = st[st[r -- sk] .refval -- sks] ,[sks, sk, r, st] → [sks, i ', r, st] ,F ,storefuns , ,lookup-rec-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sks, i ', r, st)]]