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Proof step 31 from proof hassharing-validrefs-dups (previous step)

r ∈ refs0, validrefs(str, r ' + refs0, st[r -- _type] .type, st), path∃(str, r, r, 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1))
Proof step 30:
∃ refs2, refs1. refs0 = refs2 + (r + refs1), validrefs(str, r ' + refs0, st[r -- _type] .type, st), path∃(str, r, r, 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)

Rule argument

[speclemmaarg: ,r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1)) ,[refs, r] → [refs0, r] ,F ,list ,references-olista ,In ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs0, r)]]