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Proof step 98 from proof pathex-put-pathex-array-refval (previous step)

refs1 + r0 ' = r1 ' + refs0, list2set(refs1) ∩ list2set(refs) = ∅, st[r0 -- _type] .type = mkarraytype(ty), 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) ⊦ 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 insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-postfix antecedent: succedent: ¬ validrefs (str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, refs + refs0, ty, st) substlist: [st, ty, refs0, refs, str] → [st[r0 -- i ', refval(r2)], st[r1 -- _type] .type, r0 ' + refs, refs1, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- i ', refval(r2)], st[r1 -- _type] .type, r0 ' + refs, refs1, str)]]