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Proof step 15 from proof getarray-subset-02 (previous step)

st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty)), j0 < i0, 0 < i + j, 0 ≤ j0, i + j ≤ i0, 0 ≤ i, r ∈ st, st ⊆ st0, r -- _type ∈ st, is_arrayref(r, i0, st), r -- _length ∈ st, 0 ≤ i0, j0 < i + j, 0 < i0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, getarray(r, i, j, st) = getarray(r, i, j, st0), r -- j0 ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 14:
st[r -- _length] = intval(i0), st[r -- _type] = typeval(mkarraytype(ty)), j0 < i0, 0 < i + j, 0 ≤ j0, i + j ≤ i0, 0 ≤ i, r ∈ st, st ⊆ st0, r -- _type ∈ st, ∀ j. 0 ≤ j ∧ j < i0 → r -- j ' ∈ st, r -- _length ∈ st, 0 ≤ i0, j0 < i + j, 0 < i0, ∀ j0. ¬ j0 < 0 ∧ ¬ i0 ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, getarray(r, i, j, st) = getarray(r, i, j, st0), r -- j0 ' ∈ st

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [st, i0, r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0, r)]]