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Proof step 38 from proof range-copy-lower (previous step)

n5 < n4 + n1, n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar, n2 + n1 ≤ # ar2, (n + n3) + n1 ≤ # ar, (n1 + n2) + n4 ≤ # ar2, (n0 + n1 + n3) + n4 ≤ # ar0, ∀ n4. n4 < n1 → ar2[n2 + n4] = ar[(n + n3) + n4], ∀ n. n < n4 → ar2[(n1 + n2) + n] = ar0[(n0 + n1 + n3) + n] ⊦ ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])
Proof step 40:
n5 < n4 + n1, (n3 + n0) + n5 < # ar0, (n0 + n1 + n3) + n4 ≤ # ar0, (n1 + n2) + n4 ≤ # ar2, (n + n3) + n1 ≤ # ar, n2 + n1 ≤ # ar2, n + n1 + n3 ≤ # ar, n0 + n1 + n3 ≤ # ar0, n3 + n0 ≤ # ar0, n0 ≤ # ar0, ∀ n. n < n4 → ar2[(n1 + n2) + n] = ar0[(n0 + n1 + n3) + n], ∀ n4. n4 < n1 → ar2[n2 + n4] = ar[(n + n3) + n4] ⊦ ar2[n2 + n5] = ((n3 + n0) + n5 < n0 ∨ n0 + n1 + n3 ≤ (n3 + n0) + n5 ⊃ ar0[(n3 + n0) + n5];ar[((n3 + n0) + n5) + n - n0])

Rule argument

spec: array-copy name: at-copy seq: ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]) subst: [m0, m, n0, ar1, n, ar0] → [(n3 + n0) + n5, n1 + n3, n0, ar0, n, ar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic Used terms: (n3 + n0) + n5, n1 + n3, n0, ar0, n, ar