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Proof step 2 from proof subarray-mkempbuf-leq (previous step)

n1 ≤ n0 ⊦ subarray(mkempbuf(n0), 0, n1) = mkempbuf(n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(n1), subarray(mkempbuf(n0), 0, n1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → mkempbuf(n)[m] = empty; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s) Used terms: mkempbuf(n1), subarray(mkempbuf(n0), 0, n1)