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Proof step 15 from proof validrefs-put-badarrayfield-01 (previous step)

is_arraytype(st[r0 -- _type] .type), is_obj(str, r, st), junkref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, st), st[r -- _type] .type ≤ ty, 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 ' + refs, ty0, st) ⊦ fs ' = _type, fs ' = _length, r = jvmref, r = r0, junkref(str, r, st[r0 -- fs ', val]), dups((st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs) .butlast), r ∈ (st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs) .butlast, validrefs(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval ' + refs, ty0, st[r0 -- fs ', val]), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), is_arraytype(st[r0 -- _type] .type), is_obj(str, r, st), junkref(str, r1, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, r1 ' + refs, ty0, st) ⊦ fs ' = _type, fs ' = _length, r = jvmref, r = r0, junkref(str, r, st[r0 -- fs ', val]), dups((r1 ' + refs) .butlast), r ∈ (r1 ' + refs) .butlast, validrefs(str, r1 ' + refs, ty0, st[r0 -- fs ', val]), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, ty0, fieldvar) '], r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) '], r1)]]