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Proof step 15 from proof arr2list-put (previous step)

n < # ar, n ≤ m0 + 1, m0 + 1 < # ar, # arr2list(ar, m0) ≤ n, # arr2list(ar, m0) < # ar, # arr2list(ar, m0) ≤ m0 + 1, ∀ n, ar, bv. n < # ar ∧ n ≤ m0 ∧ m0 < # ar → (arr2list(ar, m0)[n, bv]) = arr2list(ar[n, bv], m0) ⊦ (arr2list(ar, m0) + ar[m0 + 1] ')[n, bv] = arr2list(ar[n, bv], m0) + (ar[n, bv][m0 + 1]) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ m < # ar → # arr2list(ar, m) = m + 1
Proof step 14:
m0 < # ar, n < # ar, n ≤ m0 + 1, m0 + 1 < # ar, m0 + 1 ≤ n, m0 + 1 < # ar, m0 + 1 ≤ m0 + 1, ∀ n, ar, bv. n < # ar ∧ n ≤ m0 ∧ m0 < # ar → (arr2list(ar, m0)[n, bv]) = arr2list(ar[n, bv], m0) ⊦ (arr2list(ar, m0) + ar[m0 + 1] ')[n, bv] = arr2list(ar[n, bv], m0) + (ar[n, bv][m0 + 1]) '

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: arr2list-len antecedent: succedent: m < # ar → # arr2list(ar, m) = m + 1 substlist: [m, ar] → [m0, ar] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 4, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ¬ m < n → ¬ m + m0 < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1])], [EXTRATERMS : (m0, ar)]]