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Proof step 17 from proof okarray-substore (previous step)

st[r -- _length] = intval(i), st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _type] = typeval(mkarraytype(ty0)), j < i, r -- _length ∈ st0, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, 0 ≤ i, r ∈ st, r -- _type ∈ st0, r ∈ st0, oktype(st[r -- j '], ty, st), 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st), r -- j ' ∈ st → r -- j ' ∈ st0 ∧ st[r -- j '] = st0[r -- j '], ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ st ⊆ st0, r = jvmref, oktype(st0[r -- j '], ty, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 16:
st[r -- _length] = intval(i), st0[r -- _length] = intval(i), st0[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _type] = typeval(mkarraytype(ty0)), j < i, r -- _length ∈ st0, is_arrayref(r, i, st), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, 0 ≤ i, r ∈ st, r -- _type ∈ st0, r ∈ st0, oktype(st[r -- j '], ty, st), 0 ≤ j, 0 < i, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st), r -- j ' ∈ st → r -- j ' ∈ st0 ∧ st[r -- j '] = st0[r -- j '], ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk], r = jvmref, oktype(st0[r -- j '], ty, st0)

Rule argument

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

Additional information

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