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View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 4 from proof pathex-trans (previous step)

validrefs(str, r ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 = [], ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = refs0 .last ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st)

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 2, [QUANTTERMLIST : (r ' + refs0)]]

Additional information

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