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Proof step 11 from proof nonnullrefs-dups-firstoc (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ vals0, vals1. vals = vals0 + (refval(r) + vals1) ∧ ¬ refval(r) ∈ vals0)
Proof step 10:
r0 ≠ jvmref ∧ (∃ vals2, vals1. vals0 = vals2 + (refval(r0) + vals1) ∧ ¬ refval(r0) ∈ vals2) ⊦ r0 = jvmref, dups(vals0 .nonnullrefs), ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1, ∃ r, vals, vals1, vals2. refval(r0) ' + vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: nonnullrefs-in-firstoc antecedent: succedent: r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ vals0, vals1. vals = vals0 + (refval(r) + vals1) ∧ ¬ refval(r) ∈ vals0) substlist: [vals, r] → [vals0, r0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (vals0, r0)]]