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Proof step 11 from proof junkrefs-put-refval-02 (previous step)

st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r4), junkrefs(str, r4 ' + refs, ty1, st[r -- i ', refval(r0)]), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty, mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, ∀ st0, r2, r3, str0, ty0, i0. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, r4 ' + refs, ty0, st0[r3 -- i0 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, r4 ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r = jvmref, r0 = jvmref, r1 = jvmref, junkrefs(str, r1 ' + r4 ' + refs, ty, st), junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st)))
Proof step 10:
is_obj(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty, st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r4), junkrefs(str, r4 ' + refs, ty1, st[r -- i ', refval(r0)]), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), is_obj(str, r1, st), st[r1 -- _type] .type ≤ ty, mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, ∀ st0, r2, r3, str0, ty0, i0. mkarraytype(st0[r2 -- _type] .type) ≤ st0[r3 -- _type] .type ∧ junkrefs(str0, r4 ' + refs, ty0, st0[r3 -- i0 ', refval(r2)]) → r3 = jvmref ∨ r2 = jvmref ∨ junkrefs(str0, r4 ' + refs, ty0, st0) ∨ junkref(str0, r2, st0) ⊦ r = jvmref, r0 = jvmref, r1 = jvmref, r4 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ (r4 ' + refs) .first = st[r1 -- fs '] .refval ∧ junkrefs(str, r4 ' + refs, fs .type, st)), junkref(str, r0, st)

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st, ty, r4 ' + refs, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, r4 ' + refs, r1, str)]]