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Proof step 110 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, (r ' + refs0) .last ∈ refs0

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] → [refs0, 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 ≠ []], [CSIMPNAMEDSEQ : list, references, app, ⊦ refs + [] = refs], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list-last, references, l, ⊦ r ' .last = r])], [EXTRATERMS : (refs0, r)]]