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Proof step 22 from proof subset-len-01 (previous step)

r ∈ st, exactarray(r, ty, st0), exactreftype(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), st ⊆ st0, r ∈ st0 ⊦ r = jvmref, st0[r -- _length] .intval = st[r -- _length] .intval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ exactreftype(refval(r), ty, st) → r ∈ st
Proof step 5:
⊦ 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 21:
st[r -- _type] .type = mkarraytype(ty), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), st ⊆ st0, r ∈ st0, exactarray(r, ty, st0), r -- _type ∈ st, is_typevalue(st[r -- _type]), 0 ≤ st[r -- _length] .intval, r ∈ st ⊦ st0[r -- _length] .intval = st[r -- _length] .intval, 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))])]]