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Proof step 47 from proof pathexplus-pathex (previous step)

validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st) ⊦ refs1 = [], r = refs1 .last, r = jvmref, validrefs(str, r ' + refs1 .butlast, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, (r ' + refs1 .butlast) .last, refs1 .last, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 46:
refs1 = refs + r0 ', validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st) ⊦ refs1 = [], r = r0, r = jvmref, validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, (r ' + refs) .last, r0, st)

Rule argument

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

Additional information

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