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Proof step 9 from proof validrefs-not-in-01 (previous step)

is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty0, fieldvar) ']), validrefs(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st), r ∈ refs, ∀ r1, str0, ty1, st0. (r1 = st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ∨ r1 ∈ refs) ∧ validrefs(str0, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty1, st0) → r1 = jvmref ∨ is_valid_ref(str0, r1, st0) ⊦ r0 = jvmref, r = r0, r = jvmref, r = st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, is_valid_ref(str, r, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), is_referencevalue(st[r0 -- mkfs(class, ty0, fieldvar) ']), validrefs(str, r2 ' + refs, ty0, st), r ∈ refs, ∀ r1, str0, ty1, st0. (r1 = r2 ∨ r1 ∈ refs) ∧ validrefs(str0, r2 ' + refs, ty1, st0) → r1 = jvmref ∨ is_valid_ref(str0, r1, st0) ⊦ r0 = jvmref, r = r0, r = jvmref, r = r2, is_valid_ref(str, r, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r0 -- mkfs(class, ty0, fieldvar) '], r2] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r0 -- mkfs(class, ty0, fieldvar) '], r2)]]