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Proof step 16 from proof disjoint-def-pathex (previous step)

(r2 ' + refs2) .last = (r3 ' + refs1) .last, validrefs(str, r3 ' + refs1, st[r3 -- _type] .type, st), validrefs(str, r2 ' + refs2, st[r2 -- _type] .type, st), r3 ∈ refs, r2 ∈ refs ⊦ (r3 ' + refs1) .last = jvmref, r2 = r3, ∃ refs0. refs0 ≠ [] ∧ refs0 .first = r3 ∧ refs0 .last = (refs0 .first ' + refs1) .last ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

[EXRARG : pos: right 3, [QUANTTERMLIST : (r3 ' + refs1)]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])], [EXTRATERMS : (r3 ' + refs1)]]