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Proof step 63 from proof validrefs-subset (previous step)

st[r0 -- _length] = st0[r0 -- _length], st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- i '] = refval(r), r0 -- _length ∈ st0, r0 ∈ st0, r0 ∈ st, r0 -- _type ∈ st0, 0 ≤ i, 0 < st0[r0 -- _length] .intval, st0[r0 -- _type] .type ≤ ty, is_array(str, r0, st), is_valid_ref(str, r0, st0), i < st0[r0 -- _length] .intval, validrefs(str, r ' + refs, st0[r0 -- _type] .type .type, st0), r0 -- _type ∈ st, r0 -- _length ∈ st, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, r ' + refs, ty0, st2), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, r0 -- i ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , ¬ r -- i ' ∈ st ∧ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ r ≠ jvmref → ¬ is_array(str, r, st) ,[r, i, st, str] → [r0, i, st, str] ,F ,okfuns , ,is_array-notin-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 < i → 0 < j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (r0, i, st, str)]]