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Proof step 90 from proof pathex-put-pathex-array-refval (previous step)

refs1 + r0 ' = r1 ' + refs0, list2set(refs1) ∩ list2set(refs) = ∅, st[r0 -- _type] .type = mkarraytype(ty), refs .first = (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 elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 89:
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

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: references lemma-name: elim-list-c antecedent: refs ≠ [] succedent: r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 substlist: [refs, r, refs0] → [refs, r3, refs2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs, r3, refs2)]]