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Proof step 9 from proof nonnullrefs-dups (previous step)

r0 ∈ vals0 .nonnullrefs ⊦ r0 = jvmref, dups(vals0 .nonnullrefs), ∃ r, m, n. (refval(r0) ' + vals0)[m] = refval(r) ∧ (refval(r0) ' + vals0)[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ ¬ # vals0 < m ∧ ¬ # vals0 < n, ∃ r, m, n. vals0[m] = refval(r) ∧ vals0[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ ¬ # vals0 ≤ m ∧ ¬ # vals0 ≤ n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. vals[m] = refval(r) ∧ m < # vals)
Proof step 8:
r0 ≠ jvmref ∧ (∃ m. vals0[m] = refval(r0) ∧ m < # vals0) ⊦ r0 = jvmref, dups(vals0 .nonnullrefs), ∃ r, m, n. (refval(r0) ' + vals0)[m] = refval(r) ∧ (refval(r0) ' + vals0)[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ ¬ # vals0 < m ∧ ¬ # vals0 < n, ∃ r, m, n. vals0[m] = refval(r) ∧ vals0[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ ¬ # vals0 ≤ m ∧ ¬ # vals0 ≤ n

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: nonnullrefs-in antecedent: succedent: r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. vals[m] = refval(r) ∧ m < # vals) substlist: [vals, r] → [vals0, r0] 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 : (vals0, r0)]]