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Proof step 8 from proof subarray-subarray-elim (previous step)

n0 + n1 ≤ # ar0, m0 + m1 ≤ n1, n < m1 ⊦ m1 = 0, copy(ar0, n0, mkarray(n1), 0, n1)[n + m0] = ar0[n + n0 + m0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0])

Rule argument

spec: 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 + m0, n1, 0, mkarray(n1), n0, ar0] flags: rewrite, current

Additional information

Used simplifier rules: zero-01: ⊦ ¬ m < 0; from specification nat-basic1%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%sub-base: ⊦ m - 0 = m; from specification nat%Size-mkarray: ⊦ # mkarray(n) = n; from specification array%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%lep-02: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; from specification nat Used terms: n + m0, n1, 0, mkarray(n1), n0, ar0