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Proof step 16 from proof abs-nodes-notrailer-h (previous step)

abs-nodes(buf, n, nd ' + x0, lax, weak), is-encoded(nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf ⊦ range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 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)))
Proof step 18:
is-encoded(nodeheader(m, boolvar0), subarray(buf, 0, NODE_HEADER_SIZE)), 2 * NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE) ≤ # buf, ∃ buf0, buf1. buf = buf0 + buf1 ∧ ( abs-padding(buf0) ∧ abs-nodes(buf1, n + # buf0, nd ' + x0, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = n ∧ lax.head.size = # buf0 ∧ abs-node(buf0, nd) ∧ abs-nodes(buf1, n + # buf0, x0, lax.tail, weak)) ⊦ range=(buf, NODE_HEADER_SIZE + align↑(m, 2 * NODE_HEADER_SIZE), validtrailer, 0, NODE_HEADER_SIZE)

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] → [weak, lax, x0, nd, n, buf] flags: <all paths>

Additional information

Used terms: weak, lax, x0, nd, n, buf