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Proof step 11 from proof subset-len-01 (previous step)

st0[r -- _length] = intval(i0), st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty)), r -- _length ∈ st0, is_arrayref(r, i0, st0), r -- _type ∈ st, r ∈ st, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), st ⊆ st0, r -- _type ∈ st0, r ∈ st0, 0 ≤ i0 ⊦ i0 = i, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 10:
st0[r -- _length] = intval(i0), st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty)), st0[r -- _type] = typeval(mkarraytype(ty)), r -- _length ∈ st0, is_arrayref(r, i0, st0), r -- _type ∈ st, r ∈ st, 0 ≤ i, r -- _length ∈ st, is_arrayref(r, i, st), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk], r -- _type ∈ st0, r ∈ st0, 0 ≤ i0 ⊦ i0 = i, r = jvmref

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st0, st] ,F ,store ,javastore-ostorea ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st)]]