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Proof step 9 from proof isarray-keyin (previous step)

st[r -- sk] = refval(r0), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 ≤ i0, r0 -- _length ∈ st, r0 ∈ st, 0 < st[r -- (sk ' + _length ')] .intval, 0 ≤ i, i < st[r -- (sk ' + _length ')] .intval, r0 -- _type ∈ st, i0 ≤ i, i0 < st[r -- (sk ' + _length ')] .intval, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r0 -- j '], ty) ⊦ r0 = jvmref, r0 -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,st[r -- (sk ' + sk0 ')] = st[st[r -- sk] .refval -- sk0] ,[sk0, sk, r, st] → [_length, sk, r, st] ,F ,storefuns , ,lookup-two ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (_length, sk, r, st)]]