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Proof step 1 from proof subarray-append-shift-right-simp-0 (conclusion)

m ≤ # ar1 ⊦ subarray(ar0 + ar1, 0, # ar0 + m) = ar0 + subarray(ar1, 0, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: subarray-append-shift-right seq: ⊦ # ar0 ≤ m ∧ m ≤ # ar0 + # ar1 → subarray(ar0 + ar1, 0, m) = ar0 + subarray(ar1, 0, m - # ar0) subst: [m, ar1, ar0] → [# ar0 + m, ar1, ar0] flags: <all paths>

Additional information

Used simplifier rules: append-eq-left: ⊦ ar + ar0 = ar + ar1 ↔ ar0 = ar1;%append-a: ⊦ (ar + ar0) + ar1 = ar + ar0 + ar1;% ⊦ m + n - m = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m + n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s) Used terms: # ar0 + m, ar1, ar0