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Proof step 67 from proof abs-nodes-crash-h (previous step)

abs-nodes(buf, m, nd ' + x1, lax, true), is-aligned(n, NODE_HEADER_SIZE), n ≤ # buf, ∀ 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)) ⊦ ∃ x, lax0. x ⊑ nd ' + x1 ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf, 0, n), m, x, lax0, true)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: abs-nodes-rec seq: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, m + # buf0, a ' + x, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf0 ∧ abs-node(buf0, a) ∧ abs-nodes(buf1, m + # buf0, x, lax.tail, weak))) subst: [weak, lax, x, a, m, buf] → [true, lax, x1, nd, m, buf] flags: <all paths>

Additional information

Used terms: true, lax, x1, nd, m, buf