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Proof step 51 from proof junkrefs-null-01 (previous step)

is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, ty, st. junkrefs(str, acc + jvmref ' + refs0, ty, st) ↔ junkrefs(str, acc, ty, st) ⊦ r = jvmref, junkrefs(str, (r ' + acc) + jvmref ' + refs0, ty, st) ↔ 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ 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 50:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, ty, st. junkrefs(str, acc + jvmref ' + refs0, ty, st) ↔ junkrefs(str, acc, ty, st) ⊦ r = jvmref, acc + jvmref ' + refs0 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (acc + jvmref ' + refs0) .first = st[r -- i '] .refval ∧ junkrefs(str, acc + jvmref ' + refs0, st[r -- _type] .type .type, st)) ↔ 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))

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc + jvmref ' + refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + jvmref ' + refs0, r, str)]]