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Proof step 26 from proof hassharing-validrefs-dups (previous step)

path∃(str, r, r, st), validrefs(str, (r ' + refs1 + r ') + refs, st[r -- _type] .type, st), ∀ st, str, refs2, r0. # (r0 ' + refs2) < # (r ' + refs1 + (r + refs)) → (validrefs(str, r0 ' + refs2, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs2 ∧ ¬ dups(refs2)) ⊦ validrefs(str, r ' + refs1 + r ', st[r -- _type] .type, st), hasSharing(r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , ¬ validrefs(str, refs, ty, st) → ¬ validrefs(str, refs + refs0, ty, st) ,[st, ty, refs0, refs, str] → [st, st[r -- _type] .type, refs, r ' + refs1 + r ', str] ,F ,cyclic , ,validrefs-prefix ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, st[r -- _type] .type, refs, r ' + refs1 + r ', str)]]