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Proof step 49 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, subarray(buf, 0, n) = buf3 + buf0, n < (# buf + # buf2) + # buf1, n < # buf, abs-node(buf1, a), abs-nodes(buf2, m + # buf, [], [], false), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE), abs-padding(buf3) ∧ abs-nodes(buf0, m + # buf3, a ', @(m + # buf + # buf2, # buf1) ', boolvar) ∨ @(m + # buf + # buf2, # buf1) = @(m, # buf1) ∧ abs-node(buf3, a) ∧ abs-nodes(buf0, m + # buf3, [], [], boolvar), ∀ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
# buf5 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, subarray(buf5 + buf4 + validtrailer, 0, n) = buf3 + buf0, n < 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1, n < 2 * NODE_HEADER_SIZE + # buf4, abs-node(buf1, a), abs-nodes(buf2, 2 * NODE_HEADER_SIZE + m + # buf4, [], [], false), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf4, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf4, true), buf5), abs-padding(buf3) ∧ abs-nodes(buf0, m + # buf3, a ', @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) ', boolvar) ∨ @(2 * NODE_HEADER_SIZE + m + # buf4 + # buf2, # buf1) = @(m, # buf1) ∧ abs-node(buf3, a) ∧ abs-nodes(buf0, m + # buf3, [], [], boolvar), ∀ buf3, buf1, a, n, m, x, lax, boolvar. # buf3 < #((buf5 + buf4 + validtrailer) + 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 ⊦ buf5 + buf4 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf4 + # buf2 + # buf1

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 2 * NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%f: ⊦ m < n → n ≠ 0; (forward) 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]% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)