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Proof step 13 from proof at-copy (previous step)

n1 + n0 < # ar1, n0 < # ar1, n1 < m1, ∀ m0, ar1, ar0, n, n0. m0 < # ar1 → copy(ar0, n, ar1, n0, m1)[m0] = (m0 < n0 ∨ n0 + m1 ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]) ∨ # ar1 = 0 ⊦ m1 = 0, n0 + m1 = 0, copy(ar0, n, ar1, n0, m1)[n1 + n0] = ar0[n1 + n], # ar1 = 0, n1 = m1

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: n1 + n0, ar1, ar0, n, n0

Additional information

Used simplifier rules: l-02: ⊦ ¬ m + n < m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%eq-01: ⊦ m + n - m = n; from specification nat Used terms: n1 + n0, ar1, ar0, n, n0