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Proof step 30 from proof validrefs-put-notin-03 (previous step)

mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs1, ty0, st), is_obj(str, r, st), is_valid_ref(r, st), is_obj(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty ⊦ sk = _length, sk = _type, st[r -- mkfs(class, ty0, fieldvar) '] .refval = st[r -- sk] .refval, val .refval = st[r -- mkfs(class, ty0, fieldvar) '] .refval, r = st[r -- mkfs(class, ty0, fieldvar) '] .refval, r = jvmref, st[r -- mkfs(class, ty0, fieldvar) '] .refval ∈ refs1, dups(refs1), r ∈ refs1, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- sk, val][r -- fs0 ']) ∧ st[r -- mkfs(class, ty0, fieldvar) '] .refval = (st[r -- sk, val][r -- fs0 ']) .refval ∧ validrefs(str, (st[r -- sk, val][r -- fs0 ']) .refval ' + refs1, fs0 .type, st[r -- sk, val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 29:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, r0 ' + refs1, ty0, st), is_obj(str, r, st), is_valid_ref(r, st), is_obj(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty ⊦ sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, r0 ∈ refs1, dups(refs1), r ∈ refs1, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- sk, val][r -- fs0 ']) ∧ r0 = (st[r -- sk, val][r -- fs0 ']) .refval ∧ validrefs(str, (st[r -- sk, val][r -- fs0 ']) .refval ' + refs1, fs0 .type, st[r -- sk, val])

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r -- mkfs(class, ty0, fieldvar) '], r0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

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