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Proof step 21 from proof junkrefs-put-null-01 (previous step)

st[r0 -- mkfs(class0, ty2, fieldvar0) '] = refval(r2), junkrefs(str, r2 ' + refs, ty2, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_reftype(ty0), is_obj(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), mkfs(class0, ty2, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), ∀ str0, ty1, st0, fs0, r1. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_reftype(fs0 .type) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs0 ', refval(jvmref)]), r0 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ', r0 ≠ r ∨ class0 ≠ class ∨ ty2 ≠ ty0 ∨ fieldvar0 ≠ fieldvar ⊦ r0 = jvmref, junkrefs(str, r0 ' + r2 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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 20:
is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, st[r0 -- mkfs(class0, ty2, fieldvar0) '] = refval(r2), junkrefs(str, r2 ' + refs, ty2, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), is_reftype(ty0), is_obj(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), mkfs(class0, ty2, fieldvar0) ' ∈ instfields(st[r0 -- _type] .type .class), ∀ str0, ty1, st0, fs0, r1. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ is_reftype(fs0 .type) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r1 -- fs0 ', refval(jvmref)]), r0 ≠ r ∨ _type ≠ mkfs(class, ty0, fieldvar) ', r0 ≠ r ∨ class0 ≠ class ∨ ty2 ≠ ty0 ∨ fieldvar0 ≠ fieldvar ⊦ r0 = jvmref, r2 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ (r2 ' + refs) .first = st[r0 -- fs '] .refval ∧ junkrefs(str, r2 ' + refs, fs .type, st))

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st, ty, r2 ' + refs, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, r2 ' + refs, r0, str)]]