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Proof step 57 from proof nonnullrefs-dups (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 44:
dups(vals0 .nonnullrefs), ¬ 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) ⊦ ∃ r, m, n. (val ' + vals0)[m] = refval(r) ∧ (val ' + vals0)[n] = refval(r) ∧ r ≠ jvmref ∧ m ≠ n ∧ ¬ # vals0 < m ∧ ¬ # vals0 < n
Proof step 56:
∃ 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)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]