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Proof step 6 from proof at-copy (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 7:
m0 < # ar1, ∀ 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 ⊦ m0 = n0 + m1, # ar1 = 0, copy(ar0, n, ar1, n0, m1)[n0 + m1, ar0[n + m1]][m0] = (m0 < n0 ∨ n0 + m1 < m0 ⊃ ar1[m0];ar0[m0 + n - n0])

Rule argument

fma: m0 = n0 + m1

Additional information

Used simplifier rules: size-copy: ⊦ # copy(ar, m, ar0, m0, n) = # ar0;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%cgetput: m < # ar ⊦ ar[m, a][m] = a; from specification array%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%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%eq-01: ⊦ m + n - m = n; from specification nat Used formulas: m0 = n0 + m1