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Proof step 21 from proof nonnullrefs-dups (previous step)

(refval(r) ' + vals0)[n] = refval(r), n ≤ # vals0 ⊦ 0 = n, r = jvmref, dups(vals0 .nonnullrefs), r ∈ vals0 .nonnullrefs, ∃ r1, m0, n0. vals0[m0] = refval(r1) ∧ vals0[n0] = refval(r1) ∧ r1 ≠ jvmref ∧ m0 ≠ n0 ∧ ¬ # vals0 ≤ m0 ∧ ¬ # vals0 ≤ n0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
n ≠ 0 ⊦ (val ' + vals)[(* n)] = vals[n -1]
Proof step 20:
n ≠ 0, vals0[n -1] = refval(r), n ≤ # vals0 ⊦ 0 = n, r = jvmref, dups(vals0 .nonnullrefs), r ∈ vals0 .nonnullrefs, ∃ r1, m0, n0. vals0[m0] = refval(r1) ∧ vals0[n0] = refval(r1) ∧ r1 ≠ jvmref ∧ m0 ≠ n0 ∧ ¬ # vals0 ≤ m0 ∧ ¬ # vals0 ≤ n0

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: javavalues lemma-name: get-numrec antecedent: n ≠ 0 succedent: (val ' + vals)[(* n)] = vals[n -1] substlist: [n, vals, val] → [n, vals0, refval(r)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list-del, javavalues, get-zero-01, ⊦ (val ' + vals)[0] = val], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : javavalue, , inj-03, ⊦ refval(r) = refval(r0) ↔ r = r0])], [EXTRATERMS : (n, vals0, refval(r))]]