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Proof step 21 from proof nonnullrefs-dups-firstoc (previous step)

refval(r0) ' + vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ⊦ r = jvmref, r0 = jvmref, refval(r) ∈ vals, refval(r) ∈ vals1, dups(vals0 .nonnullrefs), r0 ∈ vals0 .nonnullrefs, ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1, ¬ refval(r0) ∈ vals ∧ r0 ≠ r ∧ ¬ refval(r0) ∈ vals1 ∧ ¬ refval(r0) ∈ vals2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: list instance-name: javavalues lemma-name: firsteq antecedent: vals ≠ [] succedent: val ' + vals0 = vals + vals1 ↔ val = vals .first ∧ vals0 = vals .rest + vals1 substlist: [vals1, vals, vals0, val] → [refval(r) ' + vals1 + refval(r) ' + vals2, vals, vals0, refval(r0)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refval(r) ' + vals1 + refval(r) ' + vals2, vals, vals0, refval(r0))]]