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Proof step 30 from proof validrefs-subset-equiv (previous step)

st0[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), r -- _type ∈ st, validrefs(str, r0 ' + refs1, ty0, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st ⊆ st0, st[r -- _type] .type ≤ ty, is_obj(str, r, st), r ∈ st, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs1, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk]
Proof step 29:
r -- mkfs(class, ty0, fieldvar) ' ∈ st ∧ st ⊆ st0, st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), r -- _type ∈ st, validrefs(str, r0 ' + refs1, ty0, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st ⊆ st0, st[r -- _type] .type ≤ ty, is_obj(str, r, st), r ∈ st, ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, junkref(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∧ r0 = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs1, ty0, st)

Rule argument

[speclemmaarg: ,rk ∈ st ∧ st ⊆ st1 → st1[rk] = st[rk] ,[rk, st, st1] → [r -- mkfs(class, ty0, fieldvar) ', st, st0] ,F ,store ,javastore-ostorea ,superset-elem-eq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r -- sk ∈ st ∧ sk ∈ instfields (st[r -- _type] .type .class) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (r -- mkfs(class, ty0, fieldvar) ', st, st0)]]