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Proof step 13 from proof junkrefs-levelsubset (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str0, r0 ' + refs, ty1, st), level⊆(str, str0), st[r -- _type] .type ≤ ty, is_obj(str0, r, st), is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ str1, str2, ty0, st0. level⊆(str1, str2) ∧ junkrefs(str2, r0 ' + refs, ty0, st0) → junkrefs(str1, r0 ' + refs, ty0, st0) ⊦ r = jvmref, junkrefs(str, r ' + r0 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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 12:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str0, r0 ' + refs, ty1, st), level⊆(str, str0), st[r -- _type] .type ≤ ty, is_obj(str0, r, st), is_obj(str, r, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), ∀ str1, str2, ty0, st0. level⊆(str1, str2) ∧ junkrefs(str2, r0 ' + refs, ty0, st0) → junkrefs(str1, r0 ' + refs, ty0, st0) ⊦ r = jvmref, r0 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs) .first = st[r -- fs '] .refval ∧ junkrefs(str, r0 ' + refs, fs .type, st))

Rule argument

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

Additional information

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