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Proof step 43 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < (# buf + # buf2) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf + buf2 + buf1, 0, n), m, a ', @(m + # buf + # buf2, # buf1) ', boolvar), abs-nodes(buf2, m + # buf, [], [], false), abs-padding(buf), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + buf2) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ n = (# buf + # buf2) + # buf1, # buf ≤ n ∧ n ≤ # buf + #(buf2 + buf1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < # buf, n < (# buf + # buf2) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf, 0, n), m, a ', @(m + # buf + # buf2, # buf1) ', boolvar), abs-nodes(buf2, m + # buf, [], [], false), abs-padding(buf), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf + buf2) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf3 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf3 + buf1, 0, n), m, x + a ', lax + @(m + # buf3, # buf1) ', boolvar) ∧ abs-nodes(buf3, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf3 + # buf1 ⊦ buf = mkbuf(0), n = (# buf + # buf2) + # buf1

Rule argument

Additional information

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