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Proof step 46 from proof junkref-addobj-01 (previous step)

is_array(str, r0, st), fis .keys = instfields(class), fis[mkfs(class0, ty, fieldvar) '] = refval(r0), mkfs(class0, ty, fieldvar) ' ∈ fis, junkrefs(str, r0 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), validfieldinits(fis, st), class+∃(str, class), newref(r, st), junkrefs(str, r0 ' + refs, ty, st) ⊦ r = jvmref, r0 = jvmref, is_abstract(class), r0 ' + refs ≠ [] ∧ (r0 ' + refs) .first = r0 ∧ junkrefs(str, r0 ' + refs, st[(r0 ' + refs) .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ 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 36:
¬ (is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty), is_array(str, r0, st), fis .keys = instfields(class), fis[mkfs(class0, ty, fieldvar) '] = refval(r0), mkfs(class0, ty, fieldvar) ' ∈ fis, junkrefs(str, r0 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), validfieldinits(fis, st), class+∃(str, class), newref(r, st), junkrefs(str, r0 ' + refs, ty, st) ⊦ r = jvmref, r0 = jvmref, is_abstract(class), r0 ' + refs ≠ [] ∧ (r0 ' + refs) .first = r0 ∧ junkrefs(str, r0 ' + refs, st[(r0 ' + refs) .first -- _type] .type, st)
Proof step 45:
is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), fis .keys = instfields(class), fis[mkfs(class0, ty, fieldvar) '] = refval(r0), mkfs(class0, ty, fieldvar) ' ∈ fis, junkrefs(str, r0 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), validfieldinits(fis, st), class+∃(str, class), newref(r, st), refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ refs .first = st[r0 -- i '] .refval ∧ junkrefs(str, refs, st[r0 -- _type] .type .type, st)) ⊦ r = jvmref, r0 = jvmref, is_abstract(class), r0 ' + refs ≠ [] ∧ (r0 ' + refs) .first = r0 ∧ junkrefs(str, r0 ' + refs, st[(r0 ' + refs) .first -- _type] .type, st)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, ty, refs, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, refs, r0, str)]]