[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 70 from proof splice-resize-less (previous step)

n < max(# ar1, n1 + m0), n < n2 + n1, # ar1 < n1 + n2, n < n1 + n2, n2 ≤ m0 ⊦ splice(ar0, n0, ar1, n1, m0)[n] = (n < n1 ⊃ (# ar1 ≤ n ⊃ zero;ar1[n]);ar0[n + n0 - n1]), m0 = 0, n2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ n1 + m ≤ # ar1 ∧ m ≠ 0 → splice(ar0, n0, ar1, n1, m) = copy(ar0, n0, ar1, n1, m)
Proof step 72:
n < n1 + n2, # ar1 < n1 + n2, n < n2 + n1, n < max(# ar1, n1 + m0), n2 ≤ m0 ⊦ splice(ar0, n0, ar1, n1, m0)[n] = (n < n1 ⊃ (# ar1 ≤ n ⊃ zero;ar1[n]);ar0[n + n0 - n1]), m0 = 0, n2 = 0, n1 + m0 ≤ # ar1 ∧ m0 ≠ 0

Rule argument

spec: <toplevel> name: splice-copy seq: ⊦ n1 + m ≤ # ar1 ∧ m ≠ 0 → splice(ar0, n0, ar1, n1, m) = copy(ar0, n0, ar1, n1, m) subst: [m, n1, ar1, n0, ar0] → [m0, n1, ar1, n0, ar0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n → max(n, m) = n; (s)%⊦ m0 < # ar1 → copy(ar0, n, ar1, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ ar1[m0];ar0[m0 + n - n0]); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m0, n1, ar1, n0, ar0