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Proof step 56 from proof nonnullrefs-dups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
(val ' + vals0)[m] = refval(r), (val ' + vals0)[n] = refval(r), n ≤ # vals0, m ≤ # vals0, ¬ is_referencevalue(val) ∨ val .refval = jvmref ⊦ m = n, r = jvmref, dups(vals0 .nonnullrefs), ∃ r0, m0, n0. vals0[m0] = refval(r0) ∧ vals0[n0] = refval(r0) ∧ r0 ≠ jvmref ∧ m0 ≠ n0 ∧ ¬ # vals0 ≤ m0 ∧ ¬ # vals0 ≤ n0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : nat, , lels, ⊦ ¬ m < n ↔ n ≤ m])]]