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Proof step 60 from proof range-copy-inner (previous step)

n1 + n4 < # ar0, n4 < n0 + n3 + m0, n1 + n3 ≤ # ar0, n2 + n3 ≤ # ar2, n + m0 ≤ # ar, (n3 + n2) + m0 ≤ # ar2, (n3 + n1) + m0 ≤ # ar0, (n3 + n2 + m0) + n0 ≤ # ar2, ((n3 + n1) + m0) + n0 ≤ # ar0, ∀ n. n < n3 → ar2[n2 + n] = ar0[n1 + n], ∀ n4. n4 < m0 → ar2[(n3 + n2) + n4] = ar[n + n4], ∀ n. n < n0 → ar2[(n3 + n2 + m0) + n] = ar0[((n3 + n1) + m0) + n] ⊦ ar2[n2 + n4] = ar[n4 + n - n3], n4 < n3, n3 + m0 ≤ n4

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
n4 < n3 + m0, n1 + n4 < # ar0, n4 < n0 + n3 + m0, n3 ≤ n4, n1 + n3 ≤ # ar0, n2 + n3 ≤ # ar2, n + m0 ≤ # ar, (n3 + n2) + m0 ≤ # ar2, (n3 + n1) + m0 ≤ # ar0, (n3 + n2 + m0) + n0 ≤ # ar2, ((n3 + n1) + m0) + n0 ≤ # ar0, ∀ n. n < n3 → ar2[n2 + n] = ar0[n1 + n], ∀ n4. n4 < m0 → ar2[(n3 + n2) + n4] = ar[n + n4], ∀ n. n < n0 → ar2[(n3 + n2 + m0) + n] = ar0[((n3 + n1) + m0) + n] ⊦ n0 + m0 = 0, ar2[n2 + n4] = ar[(n4 - n3) + n], m0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n ↔ ¬ n < m; (ss)