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Proof step 37 from proof nonnullrefs-dups (previous step)

(refval(r0) ' + vals0)[m] = refval(r), (refval(r0) ' + vals0)[n] = refval(r), n ≤ # vals0, m ≤ # vals0 ⊦ r0 = jvmref, m = n, r = jvmref, r0 ∈ vals0 .nonnullrefs, dups(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 12:
n ≠ 0 ⊦ (val ' + vals)[(* n)] = vals[n -1]
Proof step 22:
¬ m ≠ 0, (refval(r0) ' + vals0)[m] = refval(r), (refval(r0) ' + vals0)[n] = refval(r), n ≤ # vals0, m ≤ # vals0 ⊦ r0 = jvmref, m = n, r = jvmref, r0 ∈ vals0 .nonnullrefs, dups(vals0 .nonnullrefs), ∃ r1, m0, n0. vals0[m0] = refval(r1) ∧ vals0[n0] = refval(r1) ∧ r1 ≠ jvmref ∧ m0 ≠ n0 ∧ ¬ # vals0 ≤ m0 ∧ ¬ # vals0 ≤ n0
Proof step 36:
m ≠ 0, vals0[m -1] = refval(r), (refval(r0) ' + vals0)[n] = refval(r), n ≤ # vals0, m ≤ # vals0 ⊦ r0 = jvmref, m = n, r = jvmref, r0 ∈ vals0 .nonnullrefs, dups(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] → [m, vals0, refval(r0)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (m, vals0, refval(r0))]]