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Proof step 81 from proof pathex-put-pathex-array-refval (previous step)

is_array(str, r0, st) ∧ r0 ≠ (r3 ' + refs2) .last, list2set(refs1) ∩ list2set(refs2) = ∅, refs1 + r0 ' = r1 ' + refs0, st[r0 -- _type] .type = mkarraytype(ty), st[r0 -- i0 '] = refval(r3), validrefs(str, r3 ' + refs2, ty, st), i0 < st[r0 -- _length] .intval, validrefs(str, r ' + refs1 + r0 ' + r3 ' + refs2, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), path∃(str, r, r0, st), i < st[r0 -- _length] .intval, validref(str, r2, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, refs1 + r0 ' + r3 ' + refs2, st[r1 -- _type] .type, st[r0 -- i ', refval(r2)]), is_array(str, r0, st[r0 -- i ', refval(r2)]), 0 ≤ i0, r2 = jvmref → is_reftype(ty) ⊦ r = r3, r0 = r3, r = (r3 ' + refs2) .last, r0 = jvmref, r = r0, i0 = i, path∃(str, r, (r3 ' + refs2) .last, st), path∃(str, r2, (r3 ' + refs2) .last, st), r ∈ refs1, r ∈ refs2, r0 ∈ refs2, r0 ∈ refs1, r3 ∈ refs2, dups(refs2), dups(refs1), r3 ∈ refs1, ∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ ( st[r0 -- i '] .refval ≠ jvmref ∧ st[st[r0 -- i '] .refval -- _type] .type ≤ st[r0 -- _type] .type .type ∧ path∃(str, st[r0 -- i '] .refval, (r3 ' + refs2) .last, st) ∨ st[r0 -- i '] .refval = jvmref ∧ (r3 ' + refs2) .last = jvmref), ¬ r1 ∈ refs1 ∧ r1 ≠ r0, r0 ≠ r1 ∧ ¬ r0 ∈ refs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
st[r0 -- i0 '] = refval(r3), st[r0 -- _type] .type = mkarraytype(ty), refs1 + r0 ' = r1 ' + refs0, list2set(refs1) ∩ list2set(refs2) = ∅, 0 ≤ i0, is_array(str, r0, st[r0 -- i ', refval(r2)]), validrefs(str, refs1 + r0 ' + r3 ' + refs2, st[r1 -- _type] .type, st[r0 -- i ', refval(r2)]), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, path∃(str, r, r0, st), validrefs(str, r ' + refs1 + r0 ' + r3 ' + refs2, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), i0 < st[r0 -- _length] .intval, validrefs(str, r3 ' + refs2, ty, st), is_array(str, r0, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = (r3 ' + refs2) .last, i0 = i, r = r0, r0 = jvmref, r = (r3 ' + refs2) .last, r0 = r3, r = r3, r3 ∈ refs1, dups(refs1), dups(refs2), r3 ∈ refs2, r0 ∈ refs1, r0 ∈ refs2, r ∈ refs2, r ∈ refs1, path∃(str, r2, (r3 ' + refs2) .last, st), path∃(str, r, (r3 ' + refs2) .last, st), r0 ≠ r1 ∧ ¬ r0 ∈ refs0, ¬ r1 ∈ refs1 ∧ r1 ≠ r0, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r0 -- i1 ']) ∧ ( st[r0 -- i1 '] .refval ≠ jvmref ∧ st[st[r0 -- i1 '] .refval -- _type] .type ≤ ty ∧ path∃(str, st[r0 -- i1 '] .refval, (r3 ' + refs2) .last, st) ∨ st[r0 -- i1 '] .refval = jvmref ∧ (r3 ' + refs2) .last = jvmref)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javatype, , sel-01, ⊦ mkarraytype(ty) .type = ty], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i])]]