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Proof step 44 from proof nonnullrefs-dups-key (conclusion)

⊦ ¬ dups(fis .keys) → (dups(fis .vals .nonnullrefs) ↔ (∃ r, sk, sk0. sk ≠ sk0 ∧ r ≠ jvmref ∧ fis[sk] = refval(r) ∧ fis[sk0] = refval(r) ∧ sk ∈ fis ∧ sk0 ∈ fis))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ fis[sk] = refval(r) ∧ fis[sk0] = refval(r) ∧ sk ≠ sk0 ∧ sk ∈ fis ∧ sk0 ∈ fis ∧ r ≠ jvmref → dups(fis .vals .nonnullrefs)
Proof step 43:
dups(fis .vals .nonnullrefs) ⊦ dups(fis .keys), ∃ r, sk, sk0. sk ≠ sk0 ∧ r ≠ jvmref ∧ fis[sk] = refval(r) ∧ fis[sk0] = refval(r) ∧ sk ∈ fis ∧ sk0 ∈ fis

Rule argument

[emptyarg]

Additional information

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