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Proof step 175 from proof addarray-disjoint-nosharing-01 (previous step)

hasSharing(r, addarray(r, ty, vals, st)), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st) ⊦ r = jvmref, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ hasSharing(r, st) ↔ (∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2])
Proof step 174:
∃ sks1, sks2. fits(r, sks1, addarray(r, ty, vals, st)) ∧ fits(r, sks2, addarray(r, ty, vals, st)) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ (addarray(r, ty, vals, st)[r -- sks1]) .refval ≠ jvmref ∧ (addarray(r, ty, vals, st)[r -- sks1]) = (addarray(r, ty, vals, st)[r -- sks2]), disjoint(str, vals .nonnullrefs, st), validreflist(str, vals, ty, st), newref(r, st) ⊦ r = jvmref, dups(vals .nonnullrefs), hasSharing(vals .nonnullrefs, st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: hasSharing-def antecedent: succedent: hasSharing(r, st) ↔ (∃ sks1, sks2. fits(r, sks1, st) ∧ fits(r, sks2, st) ∧ sks1 ≠ sks2 ∧ sks1 ≠ [] ∧ sks2 ≠ [] ∧ st[r -- sks1] .refval ≠ jvmref ∧ st[r -- sks1] = st[r -- sks2]) substlist: [st, r] → [addarray(r, ty, vals, st), r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, ty, vals, st), r)]]