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Proof step 50 from proof range-copy-inner (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
n4 < n0 + n3 + m0, n1 + n4 < # ar0, ((n3 + n1) + m0) + n0 ≤ # ar0, (n3 + n2 + m0) + n0 ≤ # ar2, (n3 + n1) + m0 ≤ # ar0, (n3 + n2) + m0 ≤ # ar2, n + m0 ≤ # ar, n2 + n3 ≤ # ar2, n1 + n3 ≤ # ar0, ∀ n. n < n0 → ar2[(n3 + n2 + m0) + n] = ar0[((n3 + n1) + m0) + n], ∀ n4. n4 < m0 → ar2[(n3 + n2) + n4] = ar[n + n4], ∀ n. n < n3 → ar2[n2 + n] = ar0[n1 + n] ⊦ ar2[n2 + n4] = (n4 < n3 ∨ n3 + m0 ≤ n4 ⊃ ar0[n1 + n4];ar[n4 + n - n3])

Rule argument

Additional information

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