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Proof step 23 from proof nonnullrefs-dups-firstoc (previous step)

⊦ r0 = jvmref, r0 ∈ vals0 .nonnullrefs ↔ (∃ r, vals, vals1, vals2. refval(r0) ' + vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1), dups(vals0 .nonnullrefs), ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1

User applied rule cut formula

And obtained the following new goals

Proof step 12:
r0 ∈ vals0 .nonnullrefs ⊦ r0 = jvmref, r0 ∈ vals0 .nonnullrefs ↔ (∃ r, vals, vals1, vals2. refval(r0) ' + vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1), dups(vals0 .nonnullrefs), ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1
Proof step 22:
⊦ r0 ∈ vals0 .nonnullrefs, r0 = jvmref, r0 ∈ vals0 .nonnullrefs ↔ (∃ r, vals, vals1, vals2. refval(r0) ' + vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1), dups(vals0 .nonnullrefs), ∃ r, vals, vals1, vals2. vals0 = vals + refval(r) ' + vals1 + refval(r) ' + vals2 ∧ r ≠ jvmref ∧ ¬ refval(r) ∈ vals ∧ ¬ refval(r) ∈ vals1

Rule argument

[fma-arg: r0 ∈ vals0 .nonnullrefs]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (r0 ∈ vals0 .nonnullrefs)]]