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Proof step 75 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < # buf0 + # buf1, abs-node(buf1, a), abs-nodes(buf0, m, a0 ' + x0, lax, false), abs-nodes(subarray(buf0 + buf1, 0, n), m, (a0 ' + x0) + a ', lax + @(m + # buf0, # buf1) ', boolvar), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # buf0 → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ n = # buf0 + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 76:
⊦ 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 77:
# buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, n < # buf0 + # buf1, abs-node(buf1, a), abs-nodes(subarray(buf0 + buf1, 0, n), m, (a0 ' + x0) + a ', lax + @(m + # buf0, # buf1) ', boolvar), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), ∃ buf2, buf1. buf0 = buf2 + buf1 ∧ ( abs-padding(buf2) ∧ abs-nodes(buf1, m + # buf2, a0 ' + x0, lax, false) ∨ lax ≠ [] ∧ lax.head.off = m ∧ lax.head.size = # buf2 ∧ abs-node(buf2, a0) ∧ abs-nodes(buf1, m + # buf2, x0, lax.tail, false)), ∀ buf, buf1, a, n, m, x, lax, boolvar. # buf < # buf0 → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf + buf1, 0, n), m, x + a ', lax + @(m + # buf, # buf1) ', boolvar) ∧ abs-nodes(buf, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf + # buf1 ⊦ n = # buf0 + # buf1

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] → [false, lax, x0, a0, m, buf0] flags: <all paths>

Additional information

Used terms: false, lax, x0, a0, m, buf0