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Proof step 24 from proof cut (previous step)

# ar = m + 1, n ≤ m ⊦ ar = [], ar[n] = copy(ar, 1, mkarray(m + 1), 1, m)[n], n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy inst: name: at-copy seq: ⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]) subst: [m0, m, n0, ar1, n, ar0] → [n, m, 1, mkarray(m + 1), 1, ar] flags: rewrite

Additional information

Used simplifier rules: one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%succ-01: ⊦ m + 1 ≤ n ↔ m < n; from specification nat%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%add-01: ⊦ n ≤ m → m + n0 - n = (m - n) + n0; from specification nat%add-base: ⊦ n + 0 = n; from specification nat-basic2%Size-mkarray: ⊦ # mkarray(n) = n; from specification array%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2 Used terms: n, m, 1, mkarray(m + 1), 1, ar