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Proof step 10 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 = [], r ' + refs1 + refs0 ≠ [] ∧ (r ' + refs1 + refs0) .first = r ∧ (r ' + refs1 + refs0) .last = refs0 .last ∧ validrefs(str, r ' + refs1 + refs0, mkclasstype(`java.lang.Object' .class), st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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)

Rule argument

[emptyarg]

Additional information

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