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Proof step 4 from proof copy-shift-append (conclusion)

⊦ m ≤ # ar1 → copy(ar0 + ar1, # ar0, ar, n, m) = copy(ar1, 0, ar, n, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])

Rule argument

spec: array inst: name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [copy(ar1, 0, ar, n, m), copy(ar0 + ar1, # ar0, ar, n, m)] flags: rewrite

Additional information

[Concretesimprules((Csimpnamedseq(copy-append,,, # ar0 ≤ n, n + m1 ≤ # ar0 + # ar1 ⊦ copy(ar0 + ar1, n, ar2, m0, m1) = copy (ar1, n - # ar0, ar2, m0, m1)) Csimpnamedseq(append-a,,, ⊦ (ar + ar0) + ar1 = ar + ar0 + ar1) Csimpnamedseq(nat,,ler, ⊦ m ≤ m) Csimpnamedseq(nat,,lep-02, ⊦ m + n ≤ m + n0 ↔ n ≤ n0) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(nat,,zero, ⊦ m - m = 0) Csimpnamedseq(array-copy,,size-copy, ⊦ # copy(ar, m, ar0, m0, n) = # ar0) Csimpnamedseq(array-copy,,at-copy, ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0] ;ar0[m0 + n - n0] )) Csimpnamedseq(nat-basic2,,add-base, ⊦ n + 0 = n))), Extraterms((copy(ar1, 0, ar, n, m)copy(ar0 + ar1, # ar0, ar, n, m)))]