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Proof step 22 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), validrefs(str, r ' + refs, ty, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r, ty, st), is_array(str, r0, st), is_array(str, r0, st[r0 -- i ', refval(r)]), i < st[r0 -- _length] .intval, r = jvmref → is_reftype(ty) ⊦ r0 = r, r0 = (r ' + refs) .last, r0 = jvmref, r ∈ refs, dups(refs), r0 ∈ refs, path∃(str, r, (r ' + refs) .last, st), path∃(str, r0, (r ' + refs) .last, st), (r ' + refs) .last ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: list-last instance-name: references lemma-name: l-02 antecedent: succedent: refs ≠ [] → (r ' + refs) .last = refs .last substlist: [refs, r] → [refs, r] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 8, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list-last, references, lin-01, ⊦ refs .last ∈ refs ↔ refs ≠ []])], [EXTRATERMS : (refs, r)]]