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Proof step 9 from proof junkrefs-subset (previous step)

st[r -- _type] .type ≤ ty, st ⊆ st1, junkrefs(str, r ' + acc, ty, st1), is_obj(str, r, st), ∀ str, ty, st1, st. junkrefs(str, acc, ty, st1) ∧ st ⊆ st1 → junkrefs(str, acc, ty, st) ⊦ r = jvmref, st1[r -- _type] .type ≤ ty, acc ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ junkrefs(str, acc, fs .type, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 8:
st[r -- _type] .type ≤ ty, ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk], junkrefs(str, r ' + acc, ty, st1), is_obj(str, r, st), ∀ str, ty, st1, st. junkrefs(str, acc, ty, st1) ∧ st ⊆ st1 → junkrefs(str, acc, ty, st) ⊦ r = jvmref, st1[r -- _type] .type ≤ ty, acc ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ junkrefs(str, acc, fs .type, st))

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st1, st] ,F ,store ,javastore-ostorea ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, st)]]