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Proof step 58 from proof validrefs-junkrefs (previous step)

st[r -- i '] = refval(r1), r1 ' + refs1 = refs + st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval ' + refs0, is_valid_ref(str, st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval, st), r1 ∈ refs, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, validrefs(str, refs, st[r -- _type] .type .type, st), validrefs(str, r ' + refs, ty, st), is_referencevalue(st[refs .last -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[refs .last -- _type] .type .class), is_obj(refs .last, st) ⊦ r = jvmref, st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval = jvmref, refs = [], st[st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0, ∃ fs. fs ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- fs ']) ∧ st[refs .last -- mkfs(class, ty0, fieldvar) '] .refval = st[refs .last -- fs '] .refval ∧ ¬ st[st[refs .last -- fs '] .refval -- _type] .type ≤ fs .type

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
st[refs .last -- mkfs(class, ty0, fieldvar) '] = refval(r0), st[r -- i '] = refval(r1), r1 ' + refs1 = refs + r0 ' + refs0, is_valid_ref(str, r0, st), r1 ∈ refs, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r -- _type] .type ≤ ty, validrefs(str, refs, st[r -- _type] .type .type, st), validrefs(str, r ' + refs, ty, st), is_referencevalue(st[refs .last -- mkfs(class, ty0, fieldvar) ']), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[refs .last -- _type] .type .class), is_obj(refs .last, st) ⊦ r = jvmref, r0 = jvmref, refs = [], st[r0 -- _type] .type ≤ ty0, ∃ fs. fs ' ∈ instfields(st[refs .last -- _type] .type .class) ∧ is_referencevalue(st[refs .last -- fs ']) ∧ r0 = st[refs .last -- fs '] .refval ∧ ¬ st[st[refs .last -- fs '] .refval -- _type] .type ≤ fs .type

Rule argument

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

Additional information

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