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Proof step 10 from proof abs-nodes-valid-node (previous step)

abs-failed(buf), is-encoded(nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)), range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf ⊦ buf = mkbuf(0), ∃ buf0, buf1. buf = buf0 + buf1 ∧ boolvar0 ∧ abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, [], [], true)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ abs-failed(buf) ↔ # buf ≥ NODE_HEADER_SIZE ∧ is-aligned(# buf, NODE_HEADER_SIZE) ∧ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE))))

Rule argument

spec: abs-node name: abs-failed seq: ⊦ abs-failed(buf) ↔ # buf ≥ NODE_HEADER_SIZE ∧ is-aligned(# buf, NODE_HEADER_SIZE) ∧ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ ( is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE)))) subst: [buf] → [buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ n ≥ m ↔ m ≤ n; (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(n, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ is-encoded(ndhd, buf) → ¬ is-garbage-header(buf); (s)% ⊦ is-encoded(ndhd, buf) → (is-encoded(ndhd0, buf) ↔ ndhd = ndhd0); (s)% ⊦ nodeheader(m, boolvar).size = m; (s)%lfw-is-encoded-nodeheader-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification abs-node%m2 ≠ 0 ⊦ (* m2) * m + n ≤ m + n0 ↔ (m2 - 1) * m + n ≤ n0; (s)% ⊦ m0 * 1 = m0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m ≤ m + n; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s) Used terms: buf