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Proof step 55 from proof junkrefs-put-refval-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 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 54:
is_array(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), junkrefs(str, r1 ' + acc, ty, st[r -- i ', refval(r0)]), mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, st[r1 -- _type] .type ≤ ty, ∀ st, r0, r, str, ty, i. mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type ∧ junkrefs(str, acc, ty, st[r -- i ', refval(r0)]) → r = jvmref ∨ r0 = jvmref ∨ junkrefs(str, acc, ty, st) ∨ junkref(str, r0, st) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ acc .first = st[r1 -- i '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st)), junkref(str, r0, st)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc, r1, str)]]