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Proof step 16 from proof subset-len-01 (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), r -- _length ∈ st, is_arrayref(r, i, st), st ⊆ st0, r ∈ st0, exactreftype(refval(r), mkarraytype(ty), st0) ∧ r ≠ jvmref ∧ r -- _length ∈ st0 ∧ is_integervalue(st0[r -- _length]) ∧ 0 ≤ st0[r -- _length] .intval ∧ is_arrayref(r, st0[r -- _length] .intval, st0), r -- _type ∈ st, r ∈ st, 0 ≤ i ⊦ st0[r -- _length] .intval = i, r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ exactreftype(refval(r), ty, st) → r ∈ st
Proof step 8:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)
Proof step 15:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] .type = mkarraytype(ty), r -- _length ∈ st0, is_integervalue(st0[r -- _length]), is_arrayref(r, st0[r -- _length] .intval, st0), r -- _type ∈ st, r ∈ st, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), st ⊆ st0, r -- _type ∈ st0, is_typevalue(st0[r -- _type]), 0 ≤ st0[r -- _length] .intval, r ∈ st0 ⊦ st0[r -- _length] .intval = i, r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]