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Proof step 127 from proof hasSharing-dd-help (previous step)

validrefs(str, refs0 .first ' + refs + r1 ', st[refs0 .first -- _type] .type, st), validrefs(str, refs0 .last ' + refs2 + r0 ', st[refs0 .last -- _type] .type, st), validrefs(str, refs0, st[refs0 .first -- _type] .type, st), validrefs(str, (refs0 .first ' + refs) + r1 ' + refs1 + r0 ', st[refs0 .first -- _type] .type, st) ⊦ refs0 .last = r1, r0 = jvmref, r1 = r0, refs0 = [], path∃(str, r1, refs0 .last, st), path∃(str, refs0 .last, r1, st), hasSharing(refs0 .first, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 126:
refs0 = r + refs3, validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, refs0 .last ' + refs2 + r0 ', st[refs0 .last -- _type] .type, st), validrefs(str, refs0, st[r -- _type] .type, st), validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st) ⊦ refs0 .last = r1, r0 = jvmref, r1 = r0, refs0 = [], path∃(str, r1, refs0 .last, st), path∃(str, refs0 .last, r1, st), hasSharing(r, st)

Rule argument

[speclemmaarg: refs ≠ [] ,r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0 ,[refs, r, refs0] → [refs0, r, refs3] ,T ,list-data ,references ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : refs ≠ [] ⊦ r = refs .first ∧ refs0 = refs .rest ↔ refs = r + refs0])], [EXTRATERMS : (refs0, r, refs3)]]