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Proof step 34 from proof nonnullrefs-in-key (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ fis[sk] = refval(r) ∧ sk ∈ fis ∧ r ≠ jvmref → r ∈ fis .vals .nonnullrefs
Proof step 33:
r ∈ fis .vals .nonnullrefs ⊦ r = jvmref, dups(fis .keys), ∃ sk. fis[sk] = refval(r) ∧ sk ∈ fis

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : valuesfuns, , nonnullrefs-null, ⊦ ¬ jvmref ∈ vals .nonnullrefs])]]