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Proof step 140 from proof hasSharing-dd-help (previous step)

validrefs(str, r1 ' + refs1 + r0 ', st[r1 -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), path∃(str, r, r1, st), path∃(str, r, r2, st) ⊦ r1 = r0, r0 = jvmref, r2 = r1, path∃(str, r2, r1, st), path∃(str, r1, r2, st), hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st))
Proof step 139:
validrefs(str, r1 ' + refs1 + r0 ', st[r1 -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r1 ∧ validrefs(str, refs, st[r -- _type] .type, st), path∃(str, r, r2, st) ⊦ r1 = r0, r0 = jvmref, r2 = r1, path∃(str, r2, r1, st), path∃(str, r1, r2, st), hasSharing(r, st)

Rule argument

[speclemmaarg: , path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ validrefs(str, refs, st[r -- _type] .type, st)) ,[st, r0, r, str] → [st, r1, r, str] ,F ,cyclic , ,pathex-def-simple ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, r, str)]]