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Proof step 28 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

Proof step 23:
⊦ (refs + refs0) + refs1 = refs + refs0 + refs1
Proof step 27:
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)

Rule argument

[speclemmaarg: ,(refs + refs0) + refs1 = refs + refs0 + refs1 ,[refs1, refs0, refs] → [refs, r ', refs1] ,T ,list ,references-olista ,a ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs, r ', refs1)]]