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Proof step 84 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m0, m1), n < (# buf2 + # buf) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf2 + buf + buf1, 0, n), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, lax, false) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes(buf, m + # buf2, x0, lax.tail, false), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # 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 = (# buf2 + # buf) + # buf1, # buf2 ≤ n ∧ n ≤ # buf2 + #(buf + buf1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 85:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, lax.head = @(m0, m1), n < # buf2, n < (# buf2 + # buf) + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf2, 0, n), m, (a0 ' + x0) + a ', lax + @(m + # buf2 + # buf, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), abs-padding(buf2) ∧ abs-nodes(buf, m + # buf2, a0 ' + x0, lax, false) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes(buf, m + # buf2, x0, lax.tail, false), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #(buf2 + buf) → # 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 ⊦ buf2 = mkbuf(0), n = (# buf2 + # buf) + # 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)