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Proof step 46 from proof path-dups (previous step)

x1[m0] = x2 .last, (r ' + x1)[# x2] = x1[m0], # x2 ≤ m0, m0 < # x1, # x2 < # x1, reachable-n(H, # x2, r, x1[m0]), path(r ' + x2, H), path(r ' + x1, H) ⊦ x2 = [], x1 = [], path(r ' + firstn(m0 + 1, x1) + restn(m0 + 1, x1), H), path(r ' + firstn(m0 + 1, x1), H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ n ≤ # x0 → firstn(n, x0) + restn(n, x0) = x0

Rule argument

[x0lemmaarg: spec-name: list-del instance-name: reflist lemma-name: firstn-restn-eq antecedent: succedent: n ≤ # x0 → firstn(n, x0) + restn(n, x0) = x0 substlist: [x0, n] → [x1, m0 + 1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2, 1, 0, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≤ n ↔ m < n], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (x1, m0 + 1)]]