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Proof step 102 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), list2set(refs1) ∩ list2set(refs) = ∅, validrefs(str, r ' + refs1 + r0 ' + refs, 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, r2 = jvmref → is_reftype(ty) ⊦ r = (r0 ' + refs) .last, r0 = jvmref, r = r0, r0 ∈ refs, r0 ∈ refs1, dups(refs), dups(refs1), path∃(str, r, (r0 ' + refs) .last, st), path∃(str, r2, (r0 ' + refs) .last, st), r ∈ refs1, r ∈ refs

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[r -- _type] .type, refs1 + r0 ' + refs, r ', str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

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