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Proof step 123 from proof hasSharing-dd-help (previous step)

validrefs(str, r ' + refs3, st[r -- _type] .type, st), validrefs(str, refs3 .last ' + refs2 + r0 ', st[refs3 .last -- _type] .type, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ refs3 = [], refs3 .last = r1, r1 = r0, r0 = jvmref, path∃(str, refs3 .last, r1, st), path∃(str, r1, refs3 .last, st), hasSharing(r, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 122:
refs3 = refs0 + r2 ', validrefs(str, r ' + refs3, st[r -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ refs3 = [], r2 = r1, r1 = r0, r0 = jvmref, path∃(str, r2, r1, st), path∃(str, r1, r2, st), hasSharing(r, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs3, r2, refs0] ,T ,list-last ,references ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs3, r2, refs0)]]