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Proof step 47 from proof junkref-class-01 (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_reftype(ty), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ⊦ ty = abstract_type, r0 = jvmref, st[r0 -- _type] .type ≤ ty, junkrefs(str, r ' + r0 ', st[r -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 41:
⊦ 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 46:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_reftype(ty), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ⊦ ty = abstract_type, r0 = jvmref, st[r0 -- _type] .type ≤ ty, r0 ' ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 ' .first = st[r -- fs '] .refval ∧ junkrefs(str, r0 ', fs .type, st))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, r0 ', r, str)]]