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Proof step 38 from proof nonnullrefs-in (previous step)

⊦ r ∈ vals .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. vals[m] = refval(r) ∧ ¬ # vals ≤ m)

User applied rule structural induction

And obtained the following new goals

Proof step 1:
⊦ [] .nonnullrefs = []
Proof step 37:
∀ r. r ∈ vals0 .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. vals0[m] = refval(r) ∧ ¬ # vals0 ≤ m) ⊦ r ∈ (val + vals0) .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. (val + vals0)[m] = refval(r) ∧ ¬ # (val + vals0) ≤ m)

Rule argument

[VARWITHVARSEQSARG : vals, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : javavalues generated by [], +;], [CSIMPNAMEDSEQ : list, references, in-empty, ⊦ ¬ r ∈ []], [CSIMPNAMEDSEQ : list-data, javavalues, size-01, ⊦ # [] = 0], [CSIMPNAMEDSEQ : nat, , lez, ⊦ 0 ≤ m])]]