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Proof step 21 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf = a.alignedsize, # buf0 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n - NODE_HEADER_SIZE) = buf2 + buf1, n < 2 * NODE_HEADER_SIZE + a.alignedsize, is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(node-size-headerless(a), false), buf0), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), abs-padding(buf2) ∧ abs-nodes(buf1, m + # buf2, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', boolvar) ∨ abs-node(buf2, a) ∧ abs-nodes(buf1, m + # buf2, [], [], boolvar), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ buf0 + buf + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + a.alignedsize, n = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# buf0 = NODE_HEADER_SIZE, # buf = a.alignedsize, buf0 + subarray(buf + validtrailer, 0, n0) = buf2 + buf1, n = n0 + NODE_HEADER_SIZE, n < 2 * NODE_HEADER_SIZE + a.alignedsize, is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-encoded(a, subarray(buf, 0, node-size-headerless(a))), is-encoded(nodeheader(node-size-headerless(a), false), buf0), NODE_HEADER_SIZE ≤ n, abs-padding(buf2) ∧ abs-nodes(buf1, m + # buf2, a ', @(m, 2 * NODE_HEADER_SIZE + a.alignedsize) ', boolvar) ∨ abs-node(buf2, a) ∧ abs-nodes(buf1, m + # buf2, [], [], boolvar), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # mkbuf(0) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ buf0 + buf + validtrailer = mkbuf(0), n = 0, n = 2 * NODE_HEADER_SIZE + a.alignedsize

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, NODE_HEADER_SIZE, n0]

Additional information

Used simplifier rules: ⊦ 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 ↔ ¬ n < m; (ss)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (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% ⊦ m +1 = m + 1; (s)% ⊦ m + m0 < n → ¬ n + n0 < m; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, NODE_HEADER_SIZE, n0