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Proof step 14 from proof abs-nodes-crash-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf0 + # buf1, ∀ buf2, m, x, lax, n. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(subarray(buf0 + buf1, 0, n), m, [], [], true), # buf0 ≤ n ∧ n ≤ # buf0 + # buf1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
n < # buf0, abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf0 + # buf1, ∀ buf2, m, x, lax, n. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ buf0 = mkbuf(0), abs-nodes(subarray(buf0, 0, n), m, [], [], true)

Rule argument

Additional information

Used simplifier rules: ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ m < n → m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)