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Proof step 58 from proof validrefs-subset (previous step)

st[r0 -- i '] = refval(r), st0[r0 -- i '] = refval(r), st[r0 -- _type] = st0[r0 -- _type], st[r0 -- _length] = st0[r0 -- _length], r0 -- i ' ∈ st0, r0 -- _length ∈ st, r0 -- _type ∈ st, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st0), i < st0[r0 -- _length] .intval, is_valid_ref(str, r0, st0), is_array(str, r0, st), st0[r0 -- _type] .type ≤ ty, 0 < st0[r0 -- _length] .intval, 0 ≤ i, r0 -- _type ∈ st0, r0 ∈ st, r0 ∈ st0, r0 -- _length ∈ st0, r0 -- i ' ∈ st, st[r -- _type] .type ≤ st0[r0 -- _type] .type .type, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st), junkref(str, r, st), st ⊆ st0

User applied rule insert rewrite lemma

And obtained the following new goals

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)]]