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Proof step 114 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[r0 -- i ', refval(r2)]), r2 = jvmref → is_reftype(ty) ⊦ r0 = jvmref, r = (r ' + refs0) .last, path∃(str, r2, (r ' + refs0) .last, st), path∃(str, r, (r ' + refs0) .last, st), dups(refs0), r ∈ refs0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-put-notin antecedent: succedent: ¬ r ∈ refs → ( validrefs(str, refs, ty, st[r -- sk, val]) ↔ validrefs(str, refs, ty, st)) substlist: [val, sk, r, st, ty, refs, str] → [refval(r2), i ', r0, st, st[r -- _type] .type, r ' + refs0, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 6)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r2), i ', r0, st, st[r -- _type] .type, r ' + refs0, str)]]