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Proof step 24 from proof nonnullrefs-in (previous step)

¬ (¬ is_referencevalue(val) ∨ val .refval = jvmref), ∀ r0. r0 ∈ vals0 .nonnullrefs ↔ r0 ≠ jvmref ∧ (∃ m. vals0[m] = refval(r0) ∧ m < # vals0) ⊦ r ∈ (val ' + vals0) .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. (val ' + vals0)[m] = refval(r) ∧ ¬ # vals0 < m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ is_referencevalue(val) ∧ val .refval ≠ jvmref → (val ' + vals) .nonnullrefs = val .refval + vals .nonnullrefs
Proof step 23:
is_referencevalue(val), ∀ r0. r0 ∈ vals0 .nonnullrefs ↔ r0 ≠ jvmref ∧ (∃ m. vals0[m] = refval(r0) ∧ m < # vals0) ⊦ val .refval = jvmref, r = val .refval ∨ r ∈ vals0 .nonnullrefs ↔ r ≠ jvmref ∧ (∃ m. (val ' + vals0)[m] = refval(r) ∧ ¬ # vals0 < m)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPNAMEDSEQ : list, references, in-17, ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPNAMEDSEQ : list, references, in-append, ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]