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Proof step 112 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), 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 ' + refs0, st[r -- _type] .type, st), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = (r ' + refs0) .last, r0 = r, path∃(str, r2, (r ' + refs0) .last, st), path∃(str, r, (r ' + refs0) .last, st), dups(refs0), r ∈ refs0, r0 ∈ refs0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: pathex-validrefs-in antecedent: succedent: validrefs(str, r ' + refs, ty, st) ∧ r0 ∈ refs → path∃(str, r, r0, st) substlist: [str, r, refs, ty, st, r0] → [str, r, refs0, st[r -- _type] .type, st, (r ' + refs0) .last] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r, refs0, st[r -- _type] .type, st, (r ' + refs0) .last)]]