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Proof step 11 from proof arr2list-mod-high (previous step)

n0 + 1 < # ar, n0 + 1 < m, m < # ar, 2 + n0 < # ar, ∀ m, ar, bv. n0 < m ∧ m < # ar → arr2list(ar[m, bv], n0) = arr2list(ar, n0) ⊦ arr2list(ar[m, bv], n0 + 1) = arr2list(ar, n0) + ar[n0 + 1] '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n + 1 < # ar → arr2list(ar, n + 1) = arr2list(ar, n) + ar[n + 1] '
Proof step 10:
n0 + 1 < # (ar[m, bv]), n0 + 1 < # ar, n0 + 1 < m, m < # ar, 2 + n0 < # ar, ∀ m, ar, bv. n0 < m ∧ m < # ar → arr2list(ar[m, bv], n0) = arr2list(ar, n0) ⊦ arr2list(ar[m, bv], n0) + (ar[m, bv][n0 + 1]) ' = arr2list(ar, n0) + ar[n0 + 1] '

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: arr2list-rec antecedent: succedent: n + 1 < # ar → arr2list(ar, n + 1) = arr2list(ar, n) + ar[n + 1] ' substlist: [n, ar] → [n0, ar[m, bv]] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ # (ar[n, bv]) = # ar], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)])], [EXTRATERMS : (n0, ar[m, bv])]]