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Proof step 45 from proof junkref-update-equiv (previous step)

is_array(str, r, update(r0, fis, st)), st[r -- i '] = refval(r1), is_array(str, r, st), validFields(r0, fis, st), is_valid_ref(str, r0, st), i < st[r -- _length] .intval, junkrefs(str, r1 ' + acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis ⊦ r = r0, r = jvmref, ∃ i. 0 ≤ i ∧ i < (update(r0, fis, st)[r -- _length]) .intval ∧ is_referencevalue(update(r0, fis, st)[r -- i ']) ∧ (update(r0, fis, st)[r -- i ']) .refval ≠ jvmref ∧ ( ¬ (update(r0, fis, st)[(update(r0, fis, st)[r -- i ']) .refval -- _type]) .type ≤ (update(r0, fis, st)[r -- _type]) .type .type ∨ junkref(str, (update(r0, fis, st)[r -- i ']) .refval, update(r0, fis, st))), path∃(str, r, r0, st), _type ∈ fis

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
st[r -- i '] = refval(r1), validFields(r0, fis, st), is_valid_ref(str, r0, st), i < st[r -- _length] .intval, junkrefs(str, r1 ' + acc, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), ∀ r0, fis, st, str, r. validFields(r0, fis, st) ∧ is_valid_ref(str, r0, st) ∧ junkrefs(str, r ' + acc, st[r -- _type] .type, st) → junkref(str, r, update(r0, fis, st)) ∨ path∃(str, r, r0, st) ∨ _type ∈ fis ⊦ r = r0, r = jvmref, path∃(str, r, r0, st), _type ∈ fis, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i0 '] .refval, update(r0, fis, st)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ validFields(r, fis, st) → (update(r, fis, st) [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPSEQ : ⊦ r ≠ r0 → (update(r0, fis, st)[r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ validFields(r, fis, st) → (update(r, fis, st) [r0 -- _length ] ) = st[r0 -- _length]], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r, update(r0, fis, st)) ↔ is_array(str, r, st))])]]