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Proof step 7 from proof copy2append00 (previous step)

# ar0 = n0 + n, n ≤ # ar1 ⊦ copy(ar1, 0, ar0, 0, n) = subarray(ar1, 0, n) + subarray(ar0, n, n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: copy2append0 seq: ⊦ n1 ≤ # ar0 ∧ n0 + n1 ≤ # ar1 → copy(ar0, 0, ar1, n0, n1) = subarray(ar1, 0, n0) + subarray(ar0, 0, n1) + subarray(ar1, n0 + n1, # ar1 - n0 - n1) subst: [n1, n0, ar1, ar0] → [n, 0, ar0, ar1] flags: rewrite, current

Additional information

[Concretesimprules((Csimpnamedseq(append-prefix-left,,, ⊦ ar0 + ar1 = ar0 ↔ # ar1 = 0) Csimpnamedseq(append-a,,, ⊦ (ar + ar0) + ar1 = ar + ar0 + ar1) Csimpnamedseq(append-zero-left,,, ⊦ mkarray(0) + ar = ar) Csimpnamedseq(append-a,,, ⊦ (ar + ar0) + ar1 = ar + ar0 + ar1) Csimpnamedseq(append-eq-left,,, ⊦ ar + ar0 = ar + ar1 ↔ ar0 = ar1) Csimpnamedseq(array-copy,,subarray-zero, ⊦ subarray(ar, n, 0) = mkarray(0)) Csimpnamedseq(nat-basic2,,add-base, ⊦ n + 0 = n) Csimpnamedseq(nat-basic2,,a, ⊦ (m + n0) + n1 = m + n0 + n1) Csimpnamedseq(nat-basic2,,c, ⊦ m + n = n + m) Csimpnamedseq(nat,,sub-base, ⊦ m - 0 = m) Csimpnamedseq(nat,,eq-01, ⊦ m + n - m = n) Csimpnamedseq(nat-basic2,,eq, ⊦ m = m + n ↔ n = 0) Csimpnamedseq(nat,,lels-02, ⊦ m ≠ n → (m ≤ n ↔ m < n)) Csimpnamedseq(nat,,lels-01, ⊦ ¬ m ≤ n ↔ n < m) Csimpnamedforward(nat-basic1,,lf-02, ⊦ m < n ∧ m = n0 → n0 < n) Csimpnamedforward(nat-basic1,,lf, ⊦ m < n ∧ n < n0 → m +1 < n0) Csimpnamedforward(nat-basic1,,f, ⊦ m < n → n ≠ 0) Csimpnamedforward(nat-basic1,,trans-1, ⊦ n < n0 ∧ n0 < n1 → n < n1) Csimpnamedseq(nat-basic2,,l-02, ⊦ ¬ m + n < m) Csimpnamedforward(nat,,fle, ⊦ m < n ∧ n ≤ n0 → m < n0) Csimpnamedseq(array-copy,,copy-exact, # ar0 = m, # ar1 = m ⊦ copy(ar0, 0, ar1, 0, m) = ar0) Csimpnamedseq(array-copy,,subarray-elim, # ar = n ⊦ subarray(ar, 0, n) = ar) Csimpnamedseq(array-copy,,size-subarray, ⊦ # subarray(ar, m, n) = n))), Extraterms((n0ar0ar1))]