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Proof step 89 from proof pathex-put-pathex-array-refval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
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 ' + (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ' + 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 ' + (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ' + refs2, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), i0 < st[r0 -- _length] .intval, is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i0 ']), validrefs(str, (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ' + refs2, ty, st), r2 = jvmref → is_reftype(ty) ⊦ r = r0, r0 = jvmref, r = ((st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ' + refs2) .last, r0 = (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval, r = (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval, (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ∈ refs1, dups(refs1), dups(refs2), (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ∈ refs2, r0 ∈ refs1, r0 ∈ refs2, r ∈ refs2, r ∈ refs1, path∃(str, r2, ((st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ' + refs2) .last, st), path∃(str, r, ((st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ' + refs2) .last, st), r0 ≠ r1 ∧ ¬ r0 ∈ refs0, ¬ r1 ∈ refs1 ∧ r1 ≠ r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, in-06, ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPNAMEDSEQ : list-dup, references, dups-cons, ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPNAMEDSEQ : list, references, e-01, ⊦ r ' + refs ≠ []], [CSIMPNAMEDSEQ : set-union, references, int-c, ⊦ rset ∩ rset0 = rset0 ∩ rset], [CSIMPNAMEDSEQ : set-union, references, int-a, ⊦ (rset ∩ rset0) ∩ rset1 = rset ∩ rset0 ∩ rset1], [CSIMPNAMEDSEQ : setlist, references, in, ⊦ r ∈ list2set(refs) ↔ r ∈ refs], [CSIMPNAMEDSEQ : set-union, references, int-ins, ⊦ rset ∩ (rset0 ++ r) = ∅ ↔ rset ∩ rset0 = ∅ ∧ ¬ r ∈ rset], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : setlist, references, list2set-rec, ⊦ list2set(r ' + refs) = list2set(refs) ++ r], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]