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Proof step 92 from proof pathex-put-pathex-array-refval (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 91:
refs1 + r0 ' = r1 ' + refs0, list2set(refs1) ∩ list2set(refs) = ∅, st[r0 -- _type] .type = mkarraytype(ty), 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)]), r2 = jvmref → is_reftype(ty), refs = [] ∨ 0 ≤ i0 ∧ i0 < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ', refval(r2)][r0 -- i0 ']) ∧ refs .first = (st[r0 -- i ', refval(r2)][r0 -- i0 ']) .refval ∧ validrefs(str, refs, ty, st) ⊦ refs = [], r = r0, r0 = jvmref, r = (r0 ' + refs) .last, r ∈ refs, r ∈ refs1, path∃(str, r2, (r0 ' + refs) .last, st), path∃(str, r, (r0 ' + refs) .last, st), dups(refs1), dups(refs), r0 ∈ refs1, r0 ∈ refs, r0 ≠ r1 ∧ ¬ r0 ∈ refs0, ¬ r1 ∈ refs1 ∧ r1 ≠ r0

Rule argument

[fma-arg: refs = []]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : setlist, references, list2set-empty, ⊦ list2set([]) = ∅], [CSIMPNAMEDSEQ : set-union, references, int-e, ⊦ rset ∩ ∅ = ∅], [CSIMPNAMEDSEQ : set-union, references, int-a, ⊦ (rset ∩ rset0) ∩ rset1 = rset ∩ rset0 ∩ rset1], [CSIMPNAMEDSEQ : set-union, references, int-c, ⊦ rset ∩ rset0 = rset0 ∩ rset], [CSIMPNAMEDSEQ : list, references, app, ⊦ refs + [] = refs], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list-last, references, l, ⊦ r ' .last = r], [CSIMPNAMEDSEQ : list, references, in-empty, ⊦ ¬ r ∈ []], [CSIMPNAMEDSEQ : list-dup, references, e-01, ⊦ ¬ dups([])])], [EXTRAFMAS : (refs = [])]]