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Proof step 57 from proof junkrefs-union-disjoint (previous step)

st1 .refs ∩ st .refs = ∅, st1[r -- _type] .type ≤ ty, r ∈ st1, junkrefs(str, (st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '] .refval ' + acc, ty0, st1 ∪ st), is_referencevalue((st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields((st1 ∪ st)[r -- _type] .type .class), is_obj(str, r, st1), (st1 ∪ st)[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ (st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '] .refval = st1[r -- fs0 '] .refval ∧ junkrefs(str, st1[r -- fs0 '] .refval ' + acc, fs0 .type, st1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 56:
(st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), st1 .refs ∩ st .refs = ∅, st1[r -- _type] .type ≤ ty, r ∈ st1, junkrefs(str, r0 ' + acc, ty0, st1 ∪ st), is_referencevalue((st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields((st1 ∪ st)[r -- _type] .type .class), is_obj(str, r, st1), (st1 ∪ st)[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st1[r -- _type] .type .class) ∧ is_referencevalue(st1[r -- fs0 ']) ∧ r0 = st1[r -- fs0 '] .refval ∧ junkrefs(str, st1[r -- fs0 '] .refval ' + acc, fs0 .type, st1)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [(st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : ((st1 ∪ st)[r -- mkfs(class, ty0, fieldvar) '], r0)]]