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Proof step 8 from proof unchanged-pathex-append (previous step)

validrefs(str, (r ' + refs1) .last ' + refs0, mkclasstype(`java.lang.Object' .class), st), unchanged(str, r, st, st1), validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ (r ' + refs1) .last = r, path∃(str, (r ' + refs1) .last, ((r ' + refs1) .last ' + refs0) .last, st1), unchangedNorec((r ' + refs1) .last, st, st1), (r ' + refs1) .last ∈ refs0, (r ' + refs1) .last ∈ refs1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ refs ≠ [] ∧ refs .rest = [] → refs .last = refs .first

Rule argument

[x0lemmaarg: spec-name: list-last instance-name: references lemma-name: l-01 antecedent: succedent: refs ≠ [] ∧ refs .rest = [] → refs .last = refs .first substlist: [refs] → [r ' + refs1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 3, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .rest = refs], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPSEQ : ⊦ refs .last ∈ refs ↔ refs ≠ []])], [EXTRATERMS : (r ' + refs1)]]