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Proof step 33 from proof nonnullrefs-in-key (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ [] .vals = []
Proof step 32:
∀ r. r ∈ fis0 .vals .nonnullrefs → r = jvmref ∨ dups(fis0 .keys) ∨ (∃ sk. fis0[sk] = refval(r) ∧ sk ∈ fis0), r ∈ (fv + fis0) .vals .nonnullrefs ⊦ r = jvmref, dups((fv + fis0) .keys), ∃ sk. (fv + fis0)[sk] = refval(r) ∧ sk ∈ fv + fis0

Rule argument

[VARWITHVARSEQSARG : fis, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : fieldinits generated by [], +;], [CSIMPNAMEDSEQ : valuesfuns, , nonnullrefs-empty, ⊦ [] .nonnullrefs = []], [CSIMPNAMEDSEQ : list, references, in-empty, ⊦ ¬ r ∈ []])]]