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Proof step 40 from proof junkref-addobj-01 (previous step)

fis[mkfs(class0, ty, fieldvar) '] = refval(r0), fis .keys = instfields(class), st[r0 -- i '] = refval(r1), junkrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, newref(r, st), class+∃(str, class), validfieldinits(fis, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), junkrefs(str, r0 ' + r1 ' + refs0, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ fis, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i ⊦ r0 = jvmref, r = jvmref, junkrefs(str, r0 ' + r1 ' + refs0, st[r0 -- _type] .type, st), is_abstract(class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ 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 39:
is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ st[r0 -- _type] .type, fis[mkfs(class0, ty, fieldvar) '] = refval(r0), fis .keys = instfields(class), st[r0 -- i '] = refval(r1), junkrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, newref(r, st), class+∃(str, class), validfieldinits(fis, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), junkrefs(str, r0 ' + r1 ' + refs0, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ fis, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, 0 < st[r0 -- _length] .intval, 0 ≤ i ⊦ r0 = jvmref, r = jvmref, r1 ' + refs0 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ (r1 ' + refs0) .first = st[r0 -- i '] .refval ∧ junkrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st)), is_abstract(class)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, st[r0 -- _type] .type, r1 ' + refs0, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, st[r0 -- _type] .type, r1 ' + refs0, r0, str)]]