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Proof step 144 from proof hasSharing-dd-help (previous step)

r1 ' + refs0 = refs + refs1 .last ', path∃(str, r, r2, st), path∃(str, r, r1, st), validrefs(str, r2 ' + refs1, st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st) ⊦ refs1 = [], r2 = r1, refs1 .last = jvmref, hasSharing(r, st), path∃(str, r1, r2, st), path∃(str, r2, r1, st), ¬ r1 ∈ refs ∧ r1 ≠ refs1 .last, refs1 .last ≠ r1 ∧ ¬ refs1 .last ∈ refs0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 143:
refs1 = refs2 + r0 ', r1 ' + refs0 = refs + r0 ', path∃(str, r, r2, st), path∃(str, r, r1, st), validrefs(str, r2 ' + refs1, st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st) ⊦ refs1 = [], r2 = r1, r0 = jvmref, hasSharing(r, st), path∃(str, r1, r2, st), path∃(str, r2, r1, st), ¬ r1 ∈ refs ∧ r1 ≠ r0, r0 ≠ r1 ∧ ¬ r0 ∈ refs0

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r ' ,[refs, r, refs0] → [refs1, r0, refs2] ,T ,list-last ,references ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (refs1, r0, refs2)]]