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Proof step 40 from proof range-copy-lower (previous step)

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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
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] = (n1 ≤ n5 ⊃ ar0[(n3 + n0) + n5];ar[n3 + n5 + n])

Rule argument

Additional information

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