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Proof step 83 from proof validrefs-del-junkrefs (previous step)

is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, junkrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st -- r), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r = r0, r = r1, r0 = jvmref, junkref(str, r0, st), r ∈ acc, validrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ 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 82:
is_array(str, r0, st -- r) ∧ (st -- r)[r0 -- _type] .type ≤ ty, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, (r1 ' + acc) + r ' ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st -- r)[r0 -- _length] .intval ∧ is_referencevalue((st -- r)[r0 -- i ']) ∧ ((r1 ' + acc) + r ') .first = (st -- r)[r0 -- i '] .refval ∧ junkrefs(str, (r1 ' + acc) + r ', (st -- r)[r0 -- _type] .type .type, st -- r)), ∀ st, r0, ty, str, r. st[r0 -- _type] .type ≤ ty ∧ junkrefs(str, (r0 ' + acc) + r ', ty, st -- r) → r = r0 ∨ junkref(str, r0, st) ∨ r ∈ acc ∨ validrefs(str, r0 ' + acc + r ', ty, st) ⊦ r = r0, r = r1, r0 = jvmref, junkref(str, r0, st), r ∈ acc, validrefs(str, r0 ' + (r1 ' + acc) + r ', ty, st)

Rule argument

[speclemmaarg: , 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))) ,[st, ty, refs, r, str] → [st -- r, ty, (r1 ' + acc) + r ', r0, str] ,F ,junkrefs , ,junkrefs-array ]

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, (r1 ' + acc) + r ', r0, str)]]