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Proof step 23 from proof range-copy-lower (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
n5 < n4, n2 + n4 + n1 ≤ # ar2, n0 ≤ # ar0, n3 + n0 ≤ # ar0, n0 + n1 + n3 ≤ # ar0, n + n1 + n3 ≤ # ar, (n3 + n0) + n4 + n1 ≤ # ar0, ∀ n5. n5 < n4 + n1 → ar2[n2 + n5] = copy(ar, n, ar0, n0, n1 + n3)[(n3 + n0) + n5] ⊦ ar2[(n1 + n2) + n5] = ar0[(n0 + n1 + n3) + n5]

Rule argument

Additional information

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