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Proof step 22 from proof nonnullrefs-dups (previous step)

¬ m ≠ 0, (refval(r0) ' + vals0)[m] = refval(r), (refval(r0) ' + vals0)[n] = refval(r), n ≤ # vals0, m ≤ # vals0 ⊦ r0 = jvmref, m = n, r = jvmref, r0 ∈ vals0 .nonnullrefs, dups(vals0 .nonnullrefs), ∃ r1, m0, n0. vals0[m0] = refval(r1) ∧ vals0[n0] = refval(r1) ∧ r1 ≠ jvmref ∧ m0 ≠ n0 ∧ ¬ # vals0 ≤ m0 ∧ ¬ # vals0 ≤ n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
(refval(r) ' + vals0)[n] = refval(r), n ≤ # vals0 ⊦ 0 = n, r = jvmref, dups(vals0 .nonnullrefs), r ∈ vals0 .nonnullrefs, ∃ r1, m0, n0. vals0[m0] = refval(r1) ∧ vals0[n0] = refval(r1) ∧ r1 ≠ jvmref ∧ m0 ≠ n0 ∧ ¬ # vals0 ≤ m0 ∧ ¬ # vals0 ≤ n0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : nat, , lez, ⊦ 0 ≤ m], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list-del, javavalues, get-zero-01, ⊦ (val ' + vals)[0] = val])]]