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Proof step 10 from proof validrefs-primarray (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, ty, st), r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, is_primtype(ty), is_array(str, r, st), okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st)), i < st[r -- _length] .intval ⊦ r ' + r0 ' + refs = jvmref ', r = jvmref, is_reftype(ty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, ty, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_primtype(ty), is_array(str, r, st), okreftype(refval(r), mkarraytype(ty), st), r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), i < st[r -- _length] .intval, r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty) ⊦ r ' + r0 ' + refs = jvmref ', r = jvmref, is_reftype(ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_array(str, r, st) → is_integervalue(st[r -- _length])])]]