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Proof step 30 from proof junkrefs-delete-02 (previous step)

st[r0 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, is_array(str, r0, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st0, r1. junkrefs(str0, r2 ' + refs, ty0, st0) → junkrefs(str0, r2 ' + refs, ty0, st0 -- r1) ⊦ r0 = jvmref, r = r0, junkrefs(str, r0 ' + r2 ' + refs, ty, st -- r)

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, r0, st -- r) ∧ (st -- r)[r0 -- _type] .type ≤ ty, st[r0 -- i '] = refval(r2), junkrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, is_array(str, r0, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st0, r1. junkrefs(str0, r2 ' + refs, ty0, st0) → junkrefs(str0, r2 ' + refs, ty0, st0 -- r1) ⊦ r0 = jvmref, r = r0, r2 ' + refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st -- r)[r0 -- _length] .intval ∧ is_referencevalue((st -- r)[r0 -- i ']) ∧ (r2 ' + refs) .first = (st -- r)[r0 -- i '] .refval ∧ junkrefs(str, r2 ' + refs, (st -- r)[r0 -- _type] .type .type, st -- r))

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st -- r, ty, r2 ' + refs, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_array(str, r0, st -- r) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]])], [EXTRATERMS : (st -- r, ty, r2 ' + refs, r0, str)]]