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Proof step 13 from proof validrefs-nopathex (previous step)

validrefs(str, r ' + refs, ty, st), r0 ∈ refs, validrefs(str, r ' + refs, st[r -- _type] .type, st) ⊦ path∃(str, r, r0, 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, st[r -- _type] .type, st))
Proof step 12:
validrefs(str, r ' + refs, ty, st), r0 ∈ refs, validrefs(str, r ' + refs, st[r -- _type] .type, st) ⊦ ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st)

Rule argument

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

Additional information

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