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

is_obj(str, r0, st), st ⊆ st0, is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, acc .first, st2) ∧ acc ≠ [] → validrefs(str0, acc, ty0, st2), acc = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class) ∧ is_referencevalue(st0[r0 -- mkfs(class, ty1, fieldvar) ']) ∧ acc .first = st0[r0 -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, acc, ty1, st0) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty

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:
is_obj(str, r0, st), ∀ rk. rk ∈ st → rk ∈ st0 ∧ st[rk] = st0[rk], is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. validrefs(str0, acc, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, acc .first, st2) ∧ acc ≠ [] → validrefs(str0, acc, ty0, st2), acc = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class) ∧ is_referencevalue(st0[r0 -- mkfs(class, ty1, fieldvar) ']) ∧ acc .first = st0[r0 -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, acc, ty1, st0) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + acc, ty, st), st[r0 -- _type] .type ≤ ty

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)]]