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Proof step 46 from proof abs-nodes-crash-h (previous step)

is-aligned(n, NODE_HEADER_SIZE), is-aligned(# buf, NODE_HEADER_SIZE), n ≤ # buf, # 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))), ∀ buf0, m, x, lax, n. # buf0 < # buf → abs-nodes(buf0, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf0 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf0, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(subarray(buf, 0, n), m, [], [], true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
# buf1 = NODE_HEADER_SIZE, is-aligned(# buf0, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), n ≤ NODE_HEADER_SIZE + # buf0, is-garbage-header(buf1) ∨ is-encoded(ndhd, buf1) ∧ # buf0 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE), ∀ buf2, m, x, lax, n. # buf2 < #(buf1 + buf0) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(subarray(buf1 + buf0, 0, n), m, [], [], true)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%n ≠ 0 ⊦ is-aligned(n, n); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)