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Proof step 17 from proof validrefs-subset (previous step)

st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, r0 ∈ st0, r0 ∈ st, r0 -- _type ∈ st0, r0 -- _type ∈ st, is_obj(str, r0, st), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r ' + refs, ty1, st0), r0 -- mkfs(class, ty1, fieldvar) ' ∈ st0, st[r -- _type] .type ≤ ty1, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, ty1, st), junkref(str, r, st), st ⊆ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 16:
st[r0 -- _type] = st0[r0 -- _type], st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), r0 -- mkfs(class, ty1, fieldvar) ' ∈ st, r0 ∈ st0, r0 ∈ st, r0 -- _type ∈ st0, r0 -- _type ∈ st, is_obj(str, r0, st), is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r ' + refs, ty1, st0), r0 -- mkfs(class, ty1, fieldvar) ' ∈ st0, st[r -- _type] .type ≤ ty1, ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk] ⊦ r0 = jvmref, r = jvmref, validrefs(str, r ' + refs, ty1, st), junkref(str, r, st), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk]

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st0, st] ,F ,store ,javastore-ostorea ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st)]]