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Proof step 18 from proof isarray-put-array-badindex (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 17:
st[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), 0 < i0, 0 ≤ j, r0 ∈ st[r -- i ', val], r0 -- _length ∈ st, r0 ∈ st, r0 -- _type ∈ st, i < 0, 0 ≤ i0, ∀ j. 0 ≤ j ∧ j < i0 → r0 -- j ' ∈ st[r -- i ', val], r0 -- _length ∈ st[r -- i ', val], j < i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty) ⊦ r0 = jvmref, r0 -- j ' ∈ st

Rule argument

[x0lemmaarg: spec-name: storearrays instance-name: lemma-name: is_arrayref antecedent: succedent: is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) substlist: [st, i, r] → [st[r -- i ', val], i0, r0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 10)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', val], i0, r0)]]