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Proof step 24 from proof junkrefs-put-badarrayfield (previous step)

is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str, ty, st, fs, r0, val. ¬ junkrefs(str, acc, ty, st) ∧ fs ' ≠ _type ∧ is_arraytype(st[r0 -- _type] .type) ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ junkrefs(str, refs, fs .type, st)))
Proof step 8:
¬ (is_obj(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty), is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str, ty, st, fs, r0, val. ¬ junkrefs(str, acc, ty, st) ∧ fs ' ≠ _type ∧ is_arraytype(st[r0 -- _type] .type) ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + acc, ty, st)
Proof step 23:
is_obj(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_obj(str, r, st), is_arraytype(st[r0 -- _type] .type), acc ≠ [] ∧ (∃ fs0. fs0 ' ∈ instfields((st[r0 -- fs ', val][r -- _type]) .type .class) ∧ is_referencevalue(st[r0 -- fs ', val][r -- fs0 ']) ∧ acc .first = (st[r0 -- fs ', val][r -- fs0 ']) .refval ∧ junkrefs(str, acc, fs0 .type, st[r0 -- fs ', val])), st[r -- _type] .type ≤ ty, ∀ str, ty, st, fs, r0, val. ¬ junkrefs(str, acc, ty, st) ∧ fs ' ≠ _type ∧ is_arraytype(st[r0 -- _type] .type) ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _length, fs ' = _type, r = jvmref, junkrefs(str, r ' + acc, ty, st)

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st[r0 -- fs ', val], ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- fs ', val], ty, acc, r, str)]]