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Proof step 146 from proof hasSharing-dd-help (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 145:
r1 ' + refs0 = refs + r0 ' ∧ r1 ' + refs0 ≠ [], refs1 .last = r0, validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st), validrefs(str, r2 ' + refs1, st[r2 -- _type] .type, st), path∃(str, r, r1, st), path∃(str, r, r2, st) ⊦ refs1 .last = jvmref, r2 = r1, refs1 = [], 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] → [r1 ' + refs0, r0, refs] ,T ,list-last ,references ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPELIM : refs ≠ [] ⊦ r = refs .last ∧ refs0 = refs .butlast ↔ refs = refs0 + r '])], [EXTRATERMS : (r1 ' + refs0, r0, refs)]]