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Proof step 19 from proof arr2list-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ m < # ar → # arr2list(ar, m) = m + 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, 1, 1, 1)) dummy: () ]

Additional information

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