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Proof step 25 from proof arr2list-put (previous step)

n < # ar, n ≤ m0 + 1, 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] ')[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 7:
⊦ n < # x → (x + y)[n, bv] = x[n, bv] + y
Proof step 16:
¬ n < # arr2list(ar, m0), n < # ar, n ≤ m0 + 1, 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] ')[n, bv] = arr2list(ar[n, bv], m0) + (ar[n, bv][m0 + 1]) '
Proof step 24:
n < # arr2list(ar, m0), n < # ar, n ≤ m0 + 1, 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)[n, bv]) + ar[m0 + 1] ' = arr2list(ar[n, bv], m0) + (ar[n, bv][m0 + 1]) '

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: boollist lemma-name: put-app-left antecedent: succedent: n < # x → (x + y)[n, bv] = x[n, bv] + y substlist: [bv, n, y, x] → [bv, n, 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 : ()], [EXTRATERMS : (bv, n, ar[m0 + 1] ', arr2list(ar, m0))]]