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Proof step 89 from proof junkrefs-put-nopathexplus-equiv (previous step)

st[r -- i '] = refval(r1), st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), step∃(str, (r1 ' + refs2) .last, r0, st), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (r1 + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r = jvmref, sk = _type, r = r0, r1 = r0, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r1 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs2, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs2, mkclasstype(`java.lang.Object' .class), st), step∃(str, (r1 ' + refs2) .last, r0, st), junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ val, sk, r0, st0, ty, r2, str, refs0. # refs0 < # (r1 + refs1) → (junkrefs(str, r2 ' + refs0, ty, st0) → junkrefs(str, r2 ' + refs0, ty, st0[r0 -- sk, val]) ∨ sk = _type ∨ path∃+(str, r2, r0, st0)) ⊦ r1 = r0, r = r0, sk = _type, r = jvmref, junkrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), validrefs(str, r1 ' + refs2, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

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