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Proof step 3 from proof nosharing-nocycle (previous step)

validref(str, r, ty, st), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st) ⊦ hasSharing(r, st), ¬ r ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
⊦ dups(refs) ∧ validrefs(str, refs, st[refs .first -- _type] .type, st) → hasSharing(refs .first, st)

Rule argument

[LEMMAARG : hassharing-validrefs-dups, [refs, str, st] → [r ' + refs0, str, st]]

Additional information

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