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Proof step 13 from proof arr2list-put (previous step)

m0 < # ar, m0 + 1 < # ar, ∀ 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] ')[m0 + 1, bv] = arr2list(ar, m0) + bv '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ # x ≤ n → (x + y)[n, bv] = x + y[n - # x, bv]
Proof step 11:
⊦ m < # ar → # arr2list(ar, m) = m + 1
Proof step 12:
⊦ m < # ar → # arr2list(ar, m) = m + 1

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: boollist lemma-name: put-app-right antecedent: succedent: # x ≤ n → (x + y)[n, bv] = x + y[n - # x, bv] substlist: [bv, n, y, x] → [bv, m0 + 1, ar[m0 + 1] ', arr2list(ar, m0)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n ≤ m + n0 ↔ n ≤ n0], [CSIMPSEQ : ⊦ m + n - n + n1 = m - n1], [CSIMPSEQ : ⊦ m - m = 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (bv ')[0, bv0] = bv0 '], [CSIMPSEQ : ⊦ x + y = x + z ↔ y = z], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z])], [EXTRATERMS : (bv, m0 + 1, ar[m0 + 1] ', arr2list(ar, m0))]]