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Proof step 60 from proof abs-nodes-crash-h (previous step)

# buf1 = NODE_HEADER_SIZE, is-aligned(n, NODE_HEADER_SIZE), is-aligned(# buf0, NODE_HEADER_SIZE), n ≤ NODE_HEADER_SIZE + # buf0, is-garbage-header(buf1) ∨ is-encoded(nodeheader(m0, boolvar), buf1) ∧ # buf0 ≤ align↑(m0, 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)) ⊦ n = 0, ∃ buf3, buf2. buf1 + subarray(buf0, 0, n - NODE_HEADER_SIZE) = buf3 + buf2 ∧ # buf3 = NODE_HEADER_SIZE ∧ (is-garbage-header(buf3) ∨ (∃ ndhd. is-encoded(ndhd, buf3) ∧ # buf2 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE))), ∃ buf3, buf2. buf1 + subarray(buf0, 0, n - NODE_HEADER_SIZE) = buf3 + buf2 ∧ abs-padding(buf3) ∧ abs-nodes(buf2, m + # buf3, [], [], true)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, NODE_HEADER_SIZE, n0]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0 ⊦ is-aligned(n, m) → (n < m ↔ n = 0); (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, NODE_HEADER_SIZE, n0