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Proof step 5 from proof nonnullrefs-dups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
vals0[n] = refval(r), vals0[m] = refval(r), n < # vals0, m < # vals0, dups(vals0 .nonnullrefs) ⊦ r = jvmref, m = n, r0 = jvmref, vals0 = [], ∃ r, m, n. (refval(r0) ' + vals0)[m] = refval(r) ∧ (refval(r0) ' + vals0)[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ ¬ # vals0 < m ∧ ¬ # vals0 < n

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list-data, javavalues, l, ⊦ # vals = 0 ↔ vals = []], [CSIMPNAMEDFORWARD : nat-basic1, , f, ⊦ m < n → n ≠ 0], [CSIMPNAMEDSEQ : nat, , lels, ⊦ ¬ m < n ↔ n ≤ m])]]