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Proof step 15 from proof abs-padding-abs-nodes-h (previous step)

# buf1 = NODE_HEADER_SIZE, abs-nodes(buf1 + buf0 + validtrailer, m, nd ' + x0, lax, weak), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf0, true), buf1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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 17:
# buf1 = NODE_HEADER_SIZE, is-aligned(# buf0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf0, true), buf1), ∃ buf3, buf2. buf1 + buf0 + validtrailer = buf3 + buf2 ∧ ( abs-padding(buf3) ∧ abs-nodes(buf2, m + # buf3, nd ' + x0, lax, weak) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf3 ∧ abs-node(buf3, nd) ∧ abs-nodes(buf2, m + # buf3, x0, lax.tail, weak)) ⊦

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, m, buf1 + buf0 + validtrailer] flags: <all paths>

Additional information

Used terms: weak, lax, x0, nd, m, buf1 + buf0 + validtrailer