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Proof step 43 from proof range-copy-upper (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
n4 = n5 + n3, n4 < n0 + n3, n1 + n4 < # ar0, n4 < n3 + m0, n + n0 ≤ # ar, (n3 + n2) + n0 ≤ # ar2, n1 + n3 ≤ # ar0, n2 + n3 ≤ # ar2, n3 + n1 ≤ # ar0, n1 ≤ # ar0, n1 + n0 + n3 ≤ # ar0, (n3 + n1) + m0 ≤ # ar0, n + m0 ≤ # ar, n0 ≤ m0, n3 ≤ n4, ∀ n4. n4 < n0 → ar2[(n3 + n2) + n4] = ar[n + n4], ∀ n. n < n3 → ar2[n2 + n] = ar0[n1 + n] ⊦ ar2[n2 + n4] = ar[n5 + n], m0 = 0, n0 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n4, n3, n5]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n4, n3, n5