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Proof step 18 from proof pathex-trans (previous step)

path∃(str, r, r0, st), validrefs(str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 = [], path∃(str, r, refs0 .last, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st))
Proof step 17:
∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r0 ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ refs0 = [], path∃(str, r, refs0 .last, st)

Rule argument

[crewrite-arg: pathex-def, F, [st, r0, r, str] → [st, r0, r, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, r, str)]]