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Proof step 9 from proof pathex-trans (previous step)

validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), validrefs(str, refs1 .last ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs1 = [], refs0 = [], validrefs(str, r ' + refs1 + refs0, mkclasstype(`java.lang.Object' .class), st)

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ refs ≠ [] ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st) ∧ validrefs(str, refs .last + refs1, mkclasstype(`java.lang.Object' .class), st) → validrefs(str, refs + refs1, mkclasstype(`java.lang.Object' .class), st)

Rule argument

[LEMMAARG : validrefs-trans, [str, refs, st, refs1] → [str, r ' + refs1, st, refs0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPSEQ : ⊦ r + refs = r ' + refs])], [EXTRATERMS : (str, r ' + refs1, st, refs0)]]