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Proof step 19 from proof nonnullrefs-dups-firstoc (previous step)

refval(r0) = vals .first ⊦ r = jvmref, r0 = jvmref, vals = [], refval(r) ∈ vals, refval(r) ∈ vals1, dups((vals .rest + refval(r) ' + vals1 + refval(r) ' + vals2) .nonnullrefs), r0 ∈ (vals .rest + refval(r) ' + vals1 + refval(r) ' + vals2) .nonnullrefs, ∃ r0, vals5, vals4, vals3. vals .rest + refval(r) ' + vals1 + refval(r) ' + vals2 = vals5 + refval(r0) ' + vals4 + refval(r0) ' + vals3 ∧ r0 ≠ jvmref ∧ ¬ refval(r0) ∈ vals5 ∧ ¬ refval(r0) ∈ vals4, ¬ refval(r0) ∈ vals ∧ r0 ≠ r ∧ ¬ refval(r0) ∈ vals1 ∧ ¬ refval(r0) ∈ vals2

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: javavalues lemma-name: elim-list-c antecedent: vals ≠ [] succedent: val = vals .first ∧ vals0 = vals .rest ↔ vals = val + vals0 substlist: [vals, val, vals0] → [vals, val, vals0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, javavalues, c, ⊦ val + vals = val ' + vals], [CSIMPNAMEDSEQ : list, javavalues, e-01, ⊦ val ' + vals ≠ []], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list, javavalues, in-06, ⊦ ¬ val ∈ val0 ' + vals ↔ val ≠ val0 ∧ ¬ val ∈ vals], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0], [CSIMPNAMEDSEQ : list-dup, references, f-01, ⊦ dups(refs + r ' + refs0) ↔ r ∈ refs ∨ r ∈ refs0 ∨ dups(refs + refs0)], [CSIMPNAMEDSEQ : list, references, in-append, ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPNAMEDSEQ : list, references, in-06, ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPELIM : vals ≠ [] ⊦ val = vals .first ∧ vals0 = vals .rest ↔ vals = val + vals0])], [EXTRATERMS : (vals, val, vals0)]]