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Proof step 22 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs1, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, is_classtype(st[r -- _type] .type), ∀ val, sk, r, st0, ty, r2, str, refs. # refs < # (r0 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r, st0)) ⊦ r = r0, r = jvmref, sk = _type, junkrefs(str, r0 ' + refs1, ty0, st[r0 -- sk, val]), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval = r0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 21:
st[r -- _type] .type = mkclasstype(class0), st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), junkrefs(str, r0 ' + refs1, ty0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, is_classtype(st[r -- _type] .type), ∀ val, sk, r, st0, ty, r2, str, refs. # refs < # (r0 + refs1) → (junkrefs(str, r2 ' + refs, ty, st0) → junkrefs(str, r2 ' + refs, ty, st0[r -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r, st0)) ⊦ r = r0, r = jvmref, sk = _type, junkrefs(str, r0 ' + refs1, ty0, st[r0 -- sk, val]), ∃ fs. fs ' ∈ instfields(class0) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval = r0

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r -- _type] .type, class0] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r -- _type] .type, class0)]]