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Proof step 37 from proof validrefs-subset (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 36:
st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st ⊆ st0, is_valid_ref(str, r0, st0), st0[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), is_referencevalue(st0[r0 -- mkfs(class, ty1, fieldvar) ']), validrefs(str, r ' + refs, ty1, st0), ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), ∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r = st[r0 -- fs '] .refval ∧ validrefs(str, r ' + refs, fs .type, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st0[r0 -- mkfs(class, ty1, fieldvar) '], r] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st0[r0 -- mkfs(class, ty1, fieldvar) '], r)]]