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Proof step 31 from proof junkrefs-put-statfield (previous step)

is_array(str, r, st), junkrefs(str, r ' + acc, ty, st), st[r -- _type] .type ≤ ty, ∀ str, ty, st, sk, val. junkrefs(str, acc, ty, st) → junkrefs(str, acc, ty, st[jvmref -- sk, val]) ⊦ r = jvmref, acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st[jvmref -- sk, val]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 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 30:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st)), st[r -- _type] .type ≤ ty, ∀ str, ty, st, sk, val. junkrefs(str, acc, ty, st) → junkrefs(str, acc, ty, st[jvmref -- sk, val]) ⊦ r = jvmref, acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st[jvmref -- sk, val]))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r, str)]]