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Proof step 99 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf6 = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, subarray(buf3 + buf0 + validtrailer, 0, n) = buf6 + (buf5 + validtrailer) + buf2, n < 2 * NODE_HEADER_SIZE + # buf0, n < 2 * NODE_HEADER_SIZE + # buf0 + # buf + # buf1, abs-node(buf1, a), abs-nodes (buf2, 2 * NODE_HEADER_SIZE + m + # buf5, a0 ' + x0 + a ', @(m0, m1) ' + lax0 + @(2 * NODE_HEADER_SIZE + m + # buf0 + # buf, # buf1) ', boolvar), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + # buf0, a0 ' + x0, @(m0, m1) ' + lax0, false), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), is-aligned(# buf5, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf0, true), buf3), is-encoded(nodeheader(# buf5, true), buf6), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf0 + # buf + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-shift-right seq: ⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf) subst: [m, buf0, buf] → [n, buf0 + validtrailer, buf3] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s)% ⊦ 0 ≤ m; (s)%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ buf + buf0 = mkbuf(0) ↔ buf = mkbuf(0) ∧ buf0 = mkbuf(0); (ws)% ⊦ validtrailer ≠ mkbuf(0); (s) Used terms: n, buf0 + validtrailer, buf3