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Proof step 32 from proof nonnullrefs-in (previous step)

(val ' + vals0)[m] = refval(r), m ≤ # vals0, ¬ is_referencevalue(val) ∨ val .refval = jvmref ⊦ r = jvmref, r ∈ vals0 .nonnullrefs, ∃ m0. vals0[m0] = refval(r) ∧ ¬ # vals0 ≤ m0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ vals ≠ [] ∧ n ≠ 0 → vals[n] = (vals .rest)[n - 1]
Proof step 31:
val ' + vals0 ≠ [] ∧ m ≠ 0, ((val ' + vals0) .rest)[m - 1] = refval(r), m ≤ # vals0, ¬ is_referencevalue(val) ∨ val .refval = jvmref ⊦ r = jvmref, r ∈ vals0 .nonnullrefs, ∃ m0. vals0[m0] = refval(r) ∧ ¬ # vals0 ≤ m0

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: javavalues lemma-name: get-rec antecedent: succedent: vals ≠ [] ∧ n ≠ 0 → vals[n] = (vals .rest)[n - 1] substlist: [n, vals] → [m, val ' + vals0] 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, javavalues, app-02-ant, ⊦ ¬ vals + vals0 ≠ [] ↔ vals = [] ∧ vals0 = []], [CSIMPNAMEDSEQ : list, javavalues, e, ⊦ val ' ≠ []], [CSIMPNAMEDSEQ : list, javavalues, a, ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPNAMEDSEQ : list-del, javavalues, get-zero-01, ⊦ (val ' + vals)[0] = val], [CSIMPNAMEDSEQ : nat, , lez, ⊦ 0 ≤ m], [CSIMPNAMEDSEQ : javavalue, , test-19, ⊦ is_referencevalue(refval(r))], [CSIMPNAMEDSEQ : javavalue, , sel-09, ⊦ refval(r) .refval = r])], [EXTRATERMS : (m, val ' + vals0)]]