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Proof step 104 from proof hassharing-validrefs-dups (previous step)

validrefs(str, r ' + refs0, st[r -- _type] .type, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + refs0) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ hasSharing(r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , ¬ path∃(str, r, r0, st) ∧ r0 ∈ refs → ¬ validrefs(str, r ' + refs, ty, st) ,[str, r, r0, st, refs, ty] → [str, r, r, st, refs0, st[r -- _type] .type] ,F ,cyclic , ,validrefs-nopathex ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r, r, st, refs0, st[r -- _type] .type)]]