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Proof step 20 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf = a.alignedsize, # buf0 = NODE_HEADER_SIZE, buf0 + subarray(buf + validtrailer, 0, n - # buf0) = 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))), # buf0 ≤ n, n ≤ # buf0 + #(buf + validtrailer), 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# 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

Rule argument

Additional information

Used simplifier rules: m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)%m1 ≠ 0 ⊦ m ≤ (* m1) * m + n0; (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m < (* m1) * m + n0 ↔ (m1 - 1) * m + n0 ≠ 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)