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Proof step 96 from proof hassharing-validrefs-dups (previous step)

path∃(str, r, r, st), validrefs(str, r ' + r1 ' + refs1, st[r -- _type] .type, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = r1, hasSharing(r, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), r ∈ refs1, ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, refs + refs0, ty, st) ,[st, ty, refs0, refs, str] → [st, st[r -- _type] .type, r1 ' + refs1, r ', str] ,F ,cyclic , ,validrefs-postfix ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ validrefs (str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs (str, r ' + refs, ty, st)], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []])], [EXTRATERMS : (st, st[r -- _type] .type, r1 ' + refs1, r ', str)]]