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Proof step 43 from proof junkref-update-equiv (previous step)

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, ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, update(r0, fis, st)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
st[r -- i '] = refval(r1), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, junkrefs(str, r1 ' + acc, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_valid_ref(str, r0, st), validFields(r0, fis, st), st[r1 -- _type] .type ≤ st[r -- _type] .type .type, ∀ 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 = jvmref, r = r0, r1 = jvmref, _type ∈ fis, path∃(str, r, r0, st), junkref(str, r1, update(r0, fis, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ junkrefs (str, jvmref ' + refs, ty, st)], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])]]