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Proof step 18 from proof junkrefs-subset (previous step)

st1[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs, ty1, st1), mkfs(class, ty1, fieldvar) ' ∈ instfields(st1[r -- _type] .type .class), st ⊆ st1, st[r -- _type] .type ≤ ty, st1[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, ty0, st0, st2. junkrefs(str0, r0 ' + refs, ty0, st0) ∧ st2 ⊆ st0 → junkrefs(str0, r0 ' + refs, ty0, st2) ⊦ r = jvmref, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ r0 = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ junkrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 17:
r -- _type ∈ st ∧ st ⊆ st1, st1[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs, ty1, st1), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st ⊆ st1, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty, is_obj(str, r, st), ∀ str0, ty0, st0, st2. junkrefs(str0, r0 ' + refs, ty0, st0) ∧ st2 ⊆ st0 → junkrefs(str0, r0 ' + refs, ty0, st2) ⊦ r = jvmref, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ r0 = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ junkrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st)

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] ,[rk, st, st1] → [r -- _type, st, st1] ,F ,store ,javastore-ostorea ,superset-elem-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ r -- _type ∈ st → ¬ is_obj(str, r, st)])], [EXTRATERMS : (r -- _type, st, st1)]]