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Proof step 30 from proof junkrefs-levelsubset (previous step)

st[r -- i '] = refval(r0), junkrefs(str0, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), is_array(str0, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, level⊆(str, str0), ∀ str1, str2, ty0, st0. level⊆(str1, str2) ∧ junkrefs(str2, r0 ' + refs, ty0, st0) → junkrefs(str1, r0 ' + refs, ty0, st0) ⊦ r = jvmref, junkrefs(str, r ' + r0 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 29:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- i '] = refval(r0), junkrefs(str0, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), is_array(str0, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, level⊆(str, str0), ∀ str1, str2, ty0, st0. level⊆(str1, str2) ∧ junkrefs(str2, r0 ' + refs, ty0, st0) → junkrefs(str1, r0 ' + refs, ty0, st0) ⊦ r = jvmref, r0 ' + refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r0 ' + refs) .first = st[r -- i '] .refval ∧ junkrefs(str, r0 ' + refs, st[r -- _type] .type .type, st))

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, ty, r0 ' + refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r0 ' + refs, r, str)]]