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Proof step 20 from proof abs-nodes-nospace-header-h (previous step)

# buf1 + # buf0 < 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), abs-nodes(buf0, n + # buf1, nd ' + x0, @(m0, m1) ' + lax0, weak), abs-padding(buf1), is-encoded(nodeheader(m, boolvar0), subarray(buf1, 0, NODE_HEADER_SIZE)), NODE_HEADER_SIZE ≤ # buf0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: abs-node name: abs-padding seq: ⊦ abs-padding(buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(# buf1, true), buf0) ∧ is-aligned(# buf1, 2 * NODE_HEADER_SIZE)) subst: [buf] → [buf1] 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%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)%⊦ nodeheader(m, boolvar) = nodeheader(m0, boolvar0) ↔ m = m0 ∧ (boolvar ↔ boolvar0); (ws)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%m ≠ 0 ⊦ is-aligned(n, m) → n % m = 0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%m1 ≠ 0 ⊦ m + n < (* m1) * m + n0 ↔ n < (m1 - 1) * m + n0; (s)% ⊦ m0 * 1 = m0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m + m0 < n → ¬ n + n0 < m; (s) Used terms: buf1