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Proof step 3 from proof hasSharing-dd-help (previous step)

path∃(str, r, r1, st), path∃(str, r, refs0 .last, st), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st), validrefs(str, refs0 .last ', st[refs0 .last -- _type] .type, st) ⊦ refs0 = [], refs0 .last = jvmref, refs0 .last = r1, path∃(str, refs0 .last, r1, st), path∃(str, r1, refs0 .last, st), hasSharing(r, st)

User applied rule insert elim lemma

And closed the goal!

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs0, r0, refs] ,T ,list-last ,references ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ path∃(str, r, r0, st) → ¬ validrefs (str, r ' + refs + r0 ', ty, st)], [CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs0, r0, refs)]]